Datasets:
christopher
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oeis

Dataset card Data Studio Files
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348
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score
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2.47k
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int64
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666,262,453B
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timestamp
timestamp[us]date
1999-12-11 03:00:00
2026-01-19 02:46:49
filename
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29
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32
32
A000501
a(n) = floor(cosh(n)).
[ "1", "1", "3", "10", "27", "74", "201", "548", "1490", "4051", "11013", "29937", "81377", "221206", "601302", "1634508", "4443055", "12077476", "32829984", "89241150", "242582597", "659407867", "1792456423", "4872401723", "13244561064", "36002449668", "97864804714...
[ "nonn" ]
15
0
3
[ "A000471", "A000501" ]
null
N. J. A. Sloane
2022-02-01T01:00:02
oeisdata/seq/A000/A000501.seq
71284d81df973af80e7ba6ee8bd6438a
A000502
Number of genus 0 rooted maps with 6 faces and n vertices.
[ "42", "1586", "31388", "442610", "5030004", "49145460", "429166584", "3435601554", "25658464260", "181055975100", "1218601601672", "7880146275092", "49238911113224", "298652277299880", "1764885293279472", "10192638073849554", "57674223198273444", "320430129184331628", "1751190732...
[ "nonn" ]
31
5
1
[ "A000502", "A269920", "A270410" ]
[ "M5280", "N2298" ]
N. J. A. Sloane
2021-03-28T19:31:10
oeisdata/seq/A000/A000502.seq
b71698bd98a1e5013882f56b0855c632
A000503
a(n) = floor(tan(n)).
[ "0", "1", "-3", "-1", "1", "-4", "-1", "0", "-7", "-1", "0", "-226", "-1", "0", "7", "-1", "0", "3", "-2", "0", "2", "-2", "0", "1", "-3", "-1", "1", "-4", "-1", "0", "-7", "-1", "0", "-76", "-1", "0", "7", "-1", "0", "3", "-2", "0", ...
[ "sign", "easy", "nice" ]
108
0
3
[ "A000480", "A000484", "A000493", "A000494", "A000503", "A005657", "A037448", "A088306", "A195910", "A195911", "A258024", "A293698" ]
null
N. J. A. Sloane
2025-11-05T15:35:22
oeisdata/seq/A000/A000503.seq
86902f9d10fc350b44b1f4bc0e3115fd
A000504
S2(j,2j+3) where S2(n,k) is a 2-associated Stirling number of the second kind.
[ "1", "56", "1918", "56980", "1636635", "47507460", "1422280860", "44346982680", "1446733012725", "49473074851200", "1774073543492250", "66681131440423500", "2624634287988087375", "108060337458000427500", "4647703259223579555000", "208548093035794902390000", "9749651260035434678555625...
[ "nonn" ]
34
1
2
[ "A000497", "A000504", "A008299" ]
[ "M5315", "N2309" ]
N. J. A. Sloane
2025-11-05T15:35:22
oeisdata/seq/A000/A000504.seq
ae885ef1e1da804b2832f52c16536cf1
A000505
Eulerian numbers (Euler's triangle: column k=5 of A008292, column k=4 of A173018).
[ "1", "57", "1191", "15619", "156190", "1310354", "9738114", "66318474", "423281535", "2571742175", "15041229521", "85383238549", "473353301060", "2575022097600", "13796160184500", "73008517581444", "382493246941965", "1987497491971605", "10258045633638475" ]
[ "nonn", "easy" ]
75
5
2
[ "A000012", "A000460", "A000498", "A000505", "A008292", "A123125", "A173018" ]
[ "M5317", "N2310" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2024-06-02T08:18:24
oeisdata/seq/A000/A000505.seq
e0caf8296a8c133e0122e23907734551
A000506
One half of the number of permutations of [n] such that the differences have 5 runs with the same signs.
[ "61", "841", "7311", "51663", "325446", "1910706", "10715506", "58258210", "309958755", "1623847695", "8412276585", "43220104041", "220683627988", "1121561317408", "5679711010548", "28683869195556", "144552802373145", "727271783033445" ]
[ "nonn", "easy" ]
24
6
1
[ "A000506", "A008970" ]
[ "M5322", "N2313" ]
N. J. A. Sloane
2022-01-05T00:31:13
oeisdata/seq/A000/A000506.seq
befd04d8e2ad2343c6f3ec5a924de3c8
A000507
Number of permutations of [n] with exactly 3 increasing runs of length at least 2.
[ "61", "1385", "19028", "206276", "1949762", "16889786", "137963364", "1081702420", "8236142455", "61386982075", "450403628440", "3266265481144", "23480284103492", "167687984079924", "1191656966048088", "8436830209386360", "59563995267159825", "419628657826253805" ]
[ "nonn", "easy" ]
32
6
1
[ "A000507", "A008971", "A160486" ]
[ "M5323", "N2314" ]
N. J. A. Sloane
2024-11-09T17:00:31
oeisdata/seq/A000/A000507.seq
70c0167a033acfe4b197bbcb9ef70911
A000508
Generalized class numbers c_(n,3).
[ "61", "2763", "38528", "249856", "1066590", "3487246", "9493504", "22634496", "48649086", "96448478", "179369856", "315621376", "530788622", "860061996", "1346126848", "2046820352", "3038120316", "4403100222", "6254596992", "8737505280", "11992903772" ]
[ "nonn", "easy" ]
47
1
1
[ "A000003", "A000233", "A000362", "A000508", "A235605" ]
[ "M5324", "N2315" ]
N. J. A. Sloane
2024-10-25T10:05:56
oeisdata/seq/A000/A000508.seq
f8c0f671f9369e3a359b05104076aa95
A000509
Size of second largest n-arc in PG(2,q), where q runs through the primes and prime powers >= 7.
[ "6", "6", "8", "10", "12", "13", "14", "14", "17", "21", "22", "24" ]
[ "nonn", "hard", "more", "nice" ]
23
1
1
[ "A000509", "A000510", "A000961" ]
null
J. W. P. Hirschfeld [ jwph(AT)sussex.ac.uk ]
2025-11-05T15:21:39
oeisdata/seq/A000/A000509.seq
487dc14a532fb7742b0035b04f446ae3
A000510
Maximal number of points in PG(2,q) with at most 3 on a line (next term is 21 or 22).
[ "7", "9", "9", "11", "15", "15", "17" ]
[ "nonn", "hard", "more" ]
5
2
1
[ "A000509", "A000510" ]
null
J. W. P. Hirschfeld [ jwph(AT)sussex.ac.uk ]
2013-05-09T11:03:13
oeisdata/seq/A000/A000510.seq
63a1df5725df2eefb6712ebce5e46f6b
A000511
Number of n-step spiral self-avoiding walks on hexagonal lattice, where at each step one may continue in same direction or make turn of 2*Pi/3 counterclockwise.
[ "1", "1", "2", "3", "5", "8", "11", "17", "25", "33", "47", "67", "87", "117", "160", "207", "270", "356", "455", "584", "751", "945", "1195", "1513", "1882", "2345", "2927", "3608", "4446", "5483", "6701", "8180", "9986", "12109", "14664", "1775...
[ "nonn", "walk" ]
15
0
3
null
null
Stephen Penrice (penrice(AT)dimacs.rutgers.edu)
2015-09-01T06:32:54
oeisdata/seq/A000/A000511.seq
dec7ca566bd5782c774707cb98ea381e
A000512
Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 3, where equivalence is defined by row and column permutations.
[ "0", "0", "1", "1", "2", "7", "16", "51", "224", "1165", "7454", "56349", "481309", "4548786", "46829325", "519812910", "6177695783", "78190425826", "1049510787100", "14886252250208", "222442888670708", "3492326723315796", "57468395960854710", "989052970923320185", "1...
[ "nonn", "hard" ]
22
1
5
[ "A000186", "A000512", "A000513", "A000840", "A001501", "A008325", "A079815", "A133687", "A232215" ]
null
Eric Rogoyski
2020-04-04T11:04:33
oeisdata/seq/A000/A000512.seq
340b7162c1df1ecc920bac3109d4be17
A000513
Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 4, where equivalence is defined by row and column permutations. Also number of isomorphism classes of bicolored quartic bipartite graphs, where isomorphism cannot exchange the colors.
[ "0", "0", "0", "1", "1", "4", "16", "194", "3529", "121790", "5582612", "317579783", "21543414506", "1711281449485", "157117486414656", "16502328443493967", "1965612709107379155", "263512349078757245789", "39497131936385398782814", "6579940884199010139737829", "12118968740834...
[ "nonn" ]
31
1
6
[ "A000512", "A000513", "A133687" ]
null
Eric Rogoyski
2020-04-02T11:45:37
oeisdata/seq/A000/A000513.seq
bd74ab69f08eda2ca7a3aeebd7a9c9af
A000514
Eulerian numbers (Euler's triangle: column k=6 of A008292, column k=5 of A173018).
[ "1", "120", "4293", "88234", "1310354", "15724248", "162512286", "1505621508", "12843262863", "102776998928", "782115518299", "5717291972382", "40457344748072", "278794377854832", "1879708669896492", "12446388300682056", "81180715002105741", "522859244868123336", "333205833624787...
[ "nonn", "easy" ]
75
6
2
[ "A000012", "A000460", "A000498", "A000505", "A000514", "A008292", "A123125", "A173018" ]
[ "M5379", "N2336" ]
N. J. A. Sloane, Mira Bernstein, and Robert G. Wilson v
2025-01-17T10:31:08
oeisdata/seq/A000/A000514.seq
cd768bf4fc9092b56b759cca4e1e4707
A000515
a(n) = (2n)!(2n+1)!/n!^4, or equally (2n+1)*binomial(2n,n)^2.
[ "1", "12", "180", "2800", "44100", "698544", "11099088", "176679360", "2815827300", "44914183600", "716830370256", "11445589052352", "182811491808400", "2920656969720000", "46670906271240000", "745904795339462400", "11922821963004219300", "190600129650794094000", "304724898639232...
[ "nonn", "easy", "nice" ]
87
0
2
[ "A000108", "A000515", "A000894", "A002457", "A002894", "A005249", "A024492", "A039598", "A228329", "A228330", "A228331", "A228332", "A228333" ]
[ "M4874", "N2087" ]
N. J. A. Sloane
2025-11-05T15:35:22
oeisdata/seq/A000/A000515.seq
db89658d50f15c865bb0e4c00440f72a
A000516
Number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to 5, where equivalence is defined by row and column permutations. Isomorphism classes of bicolored 5-regular bipartite graphs, where isomorphism cannot exchange the colors.
[ "0", "0", "0", "0", "1", "1", "4", "51", "3529", "601055", "156473848", "54062069505", "23869437984682", "13186966476208771", "8971034249976338907", "7414924597575224629299", "7360058177440420943520750", "8683626883245180573511018830", "12066478410398147578519948851818", "19585...
[ "nonn" ]
16
1
7
[ "A000512", "A000513", "A000516", "A133687" ]
null
Eric Rogoyski
2020-04-01T14:27:14
oeisdata/seq/A000/A000516.seq
64d3ff5c926c7fce5a3b58e7d51e39ff
A000517
Number of permutations of length n with exactly three valleys.
[ "272", "7936", "137216", "1841152", "21253376", "222398464", "2174832640", "20261765120", "182172651520", "1594922762240", "13684856848384", "115620218667008", "965271355195392", "7984436548730880", "65569731961159680", "535438370914959360", "4353038473793372160", "3526678941894967...
[ "nonn" ]
38
7
1
[ "A000431", "A000487", "A000517", "A008303" ]
[ "M5431", "N2360" ]
N. J. A. Sloane
2025-11-05T15:21:39
oeisdata/seq/A000/A000517.seq
9d810ce3d3f479e78a4abd3306f3d32f
A000518
Generalized tangent numbers d_(n,4).
[ "272", "24611", "515086", "4456448", "23750912", "93241002", "296327464", "806453248", "1951153920", "4300685074", "8787223186", "16878338048", "30768878848", "53624926972", "89982082488", "146028888064", "230022888960", "353194774434", "529896144586" ]
[ "nonn" ]
33
1
1
[ "A000061", "A000176", "A000488", "A000518" ]
[ "M5432", "N2361" ]
N. J. A. Sloane
2018-05-07T22:22:46
oeisdata/seq/A000/A000518.seq
76cb014a4bbead1306bf9352b3f51d2e
A000519
Number of equivalence classes of nonzero regular 0-1 matrices of order n.
[ "1", "2", "3", "5", "7", "18", "43", "313", "7525", "846992", "324127859", "403254094631", "1555631972009429", "19731915624463099552", "791773335030637885025287", "107432353216118868234728540267", "47049030539260648478475949282317451", "71364337698829887974206671525372672234854" ]
[ "nonn" ]
25
1
2
[ "A000519", "A133687", "A333681" ]
null
Eric Rogoyski
2020-04-03T11:32:00
oeisdata/seq/A000/A000519.seq
c1ced86fc5cbf023a01bc527b0667bbd
A000520
Nearest integer to log_10(n).
[ "0", "0", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "...
[ "nonn" ]
10
1
32
null
null
N. J. A. Sloane
2019-11-08T00:25:57
oeisdata/seq/A000/A000520.seq
8bc157d2aa8f1723d78acbbb64754005
A000521
Coefficients of modular function j as power series in q = e^(2 Pi i t). Another name is the elliptic modular invariant J(tau).
[ "1", "744", "196884", "21493760", "864299970", "20245856256", "333202640600", "4252023300096", "44656994071935", "401490886656000", "3176440229784420", "22567393309593600", "146211911499519294", "874313719685775360", "4872010111798142520", "25497827389410525184", "1261429164657818430...
[ "easy", "nonn", "nice", "core" ]
264
-1
2
[ "A000521", "A005798", "A007240", "A007245", "A014708", "A027652", "A066395", "A066396", "A078906", "A091406", "A106205", "A115977", "A161361", "A161362", "A161395", "A178451", "A290403", "A290404", "A339429" ]
[ "M5477", "N2372" ]
N. J. A. Sloane
2025-11-05T15:21:39
oeisdata/seq/A000/A000521.seq
c0c92ebd3f7632113353972286bd2d2a
A000522
Total number of ordered k-tuples (k=0..n) of distinct elements from an n-element set: a(n) = Sum_{k=0..n} n!/k!.
[ "1", "2", "5", "16", "65", "326", "1957", "13700", "109601", "986410", "9864101", "108505112", "1302061345", "16926797486", "236975164805", "3554627472076", "56874039553217", "966858672404690", "17403456103284421", "330665665962404000", "6613313319248080001", "1388795797042...
[ "nonn", "easy", "nice" ]
543
0
2
[ "A000166", "A000217", "A000522", "A001338", "A001339", "A001340", "A002104", "A002627", "A006231", "A008279", "A008290", "A010844", "A010845", "A014508", "A038155", "A038159", "A054091", "A058006", "A064383", "A064384", "A068424", "A072453", "A072456", "A073591", "A08...
[ "M1497", "N0589" ]
N. J. A. Sloane
2025-12-21T12:43:54
oeisdata/seq/A000/A000522.seq
18a0843283bf2d2619ffed5d7ba1a557
A000523
a(n) = floor(log_2(n)).
[ "0", "1", "1", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "...
[ "nonn", "easy", "nice", "look" ]
200
1
4
[ "A000193", "A000195", "A000523", "A001222", "A001620", "A003462", "A004233", "A029837", "A032924", "A061168", "A070939", "A081604", "A107680", "A113473", "A152487", "A240857" ]
null
N. J. A. Sloane
2024-07-19T20:58:20
oeisdata/seq/A000/A000523.seq
11f0b02b004060dfb1e40e15bb9cc2fd
A000524
Number of rooted trees with n nodes, 2 of which are labeled.
[ "2", "9", "34", "119", "401", "1316", "4247", "13532", "42712", "133816", "416770", "1291731", "3987444", "12266845", "37627230", "115125955", "351467506", "1070908135", "3257389088", "9892759091", "30002923380", "90879555521", "274963755791", "831064788976" ]
[ "nonn", "easy", "nice" ]
38
2
1
[ "A000524", "A008295" ]
[ "M1927", "N0761" ]
N. J. A. Sloane
2023-03-23T23:09:32
oeisdata/seq/A000/A000524.seq
189e7ceac94de4ec7565cad2df2d83c7
A000525
Number of partially labeled rooted trees with n nodes (4 of which are labeled).
[ "64", "625", "4016", "21256", "100407", "439646", "1823298", "7258228", "27983518", "105146732", "386812476", "1398023732", "4977320988", "17492710572", "60790051789", "209179971147", "713533304668", "2415061934763", "8117293752058", "27111950991825", "90039381031273" ]
[ "nonn" ]
41
4
1
[ "A000525", "A008295", "A042977" ]
[ "M5329", "N2317" ]
N. J. A. Sloane
2023-03-24T09:04:37
oeisdata/seq/A000/A000525.seq
2f7ef0b095e7b613efe3d82e5a87c731
A000526
Number of partially labeled trees with n nodes (5 of which are labeled).
[ "125", "1296", "8716", "47787", "232154", "1040014", "4395772", "17781210", "69498964", "264248924", "982218072", "3582421612", "12857819052", "45515994861", "159205157535", "551049504784", "1889714853263", "6427147635062", "21698583468717" ]
[ "nonn" ]
41
5
1
[ "A000526", "A034799" ]
[ "M5387", "N2340" ]
N. J. A. Sloane
2023-03-24T09:04:24
oeisdata/seq/A000/A000526.seq
6b19553e506636f2794525f2fb940f9a
A000527
Series-parallel numbers.
[ "52", "472", "3224", "18888", "101340", "511120", "2465904", "11496144", "52165892", "231557064", "1009247192", "4331502840", "18346242492", "76822836544", "318485778848", "1308750158016", "5335993098340", "21603437175288", "86912657626392", "347660876627944", "13834573740464...
[ "nonn" ]
19
4
1
null
[ "M5304", "N2306" ]
N. J. A. Sloane
2016-02-09T07:39:40
oeisdata/seq/A000/A000527.seq
f0eb29f3d199241365e10fbc42828d81
A000528
Number of types of Latin squares of order n. Equivalently, number of nonisomorphic 1-factorizations of K_{n,n}.
[ "1", "1", "1", "2", "2", "17", "324", "842227", "57810418543", "104452188344901572", "6108088657705958932053657" ]
[ "hard", "nonn", "nice", "more" ]
30
1
4
[ "A000315", "A000479", "A000528", "A002860", "A003090", "A040082" ]
null
N. J. A. Sloane
2022-03-12T21:40:50
oeisdata/seq/A000/A000528.seq
95dff13d16f026450e7efc7562093138
A000529
Powers of rooted tree enumerator.
[ "20", "74", "186", "388", "721", "1236", "1995", "3072", "4554", "6542", "9152", "12516", "16783", "22120", "28713", "36768", "46512", "58194", "72086", "88484", "107709", "130108", "156055", "185952", "220230", "259350", "303804", "354116", "410843", "47457...
[ "nonn", "easy" ]
37
1
1
null
[ "M5086", "N2202" ]
N. J. A. Sloane
2022-04-13T13:25:15
oeisdata/seq/A000/A000529.seq
052dc230e4df9bc50f67300b19e104d3
A000530
Let p(n, s, x) be predicate that number of occurrences of s's in x >= 2*n - the length of the longest sequence of s's in x. Then a(n)=#{x in {0,1}* | x ends in 0 and p(n,0,x) and (there is no prefix y of x such that p(n,0,y) or p(n,1,y))}.
[ "1", "5", "28", "226", "2077", "20770", "222884", "2529541" ]
[ "nonn", "hard", "more" ]
13
1
2
null
null
Jonas Wallgren
2025-12-03T14:46:15
oeisdata/seq/A000/A000530.seq
0ea81181a79199ea0d95d15249e14f32
A000531
From area of cyclic polygon of 2n + 1 sides.
[ "1", "7", "38", "187", "874", "3958", "17548", "76627", "330818", "1415650", "6015316", "25413342", "106853668", "447472972", "1867450648", "7770342787", "32248174258", "133530264682", "551793690628", "2276098026922", "9373521044908", "38546133661492" ]
[ "nonn", "easy", "nice", "changed" ]
107
1
2
[ "A000531", "A002457", "A135404", "A258431" ]
null
Simon Plouffe
2026-01-17T12:49:07
oeisdata/seq/A000/A000531.seq
e1eab7dab2434b5d368d4b6b6d3475f2
A000532
Number of Hamiltonian paths from NW to SW corners in an n X n grid.
[ "1", "1", "2", "8", "86", "1770", "88418", "8934966", "2087813834", "1013346943033", "1111598871478668", "2568944901392936854", "13251059359839620127088", "145194816279817259193401518", "3524171261632305641165676374930", "182653259988707123426135593460533473" ]
[ "nonn", "walk" ]
78
1
3
[ "A000532", "A001184", "A003763", "A007764", "A014524", "A014585", "A120443", "A121785", "A121789", "A145157", "A181688", "A181689", "A271507", "A271592", "A350148", "A384173" ]
null
Russ Cox, Mar 15 1996
2025-10-31T09:23:51
oeisdata/seq/A000/A000532.seq
5add8fdb0f70d5f6280b2cd951d6afbd
A000533
a(0)=1; a(n) = 10^n + 1, n >= 1.
[ "1", "11", "101", "1001", "10001", "100001", "1000001", "10000001", "100000001", "1000000001", "10000000001", "100000000001", "1000000000001", "10000000000001", "100000000000001", "1000000000000001", "10000000000000001" ]
[ "nonn", "easy" ]
155
0
2
[ "A000533", "A002283", "A066138", "A080176", "A083318", "A138144", "A138145", "A152756", "A168624" ]
null
N. J. A. Sloane
2025-12-21T22:26:00
oeisdata/seq/A000/A000533.seq
ad35bfced17ac1663bbbf5eaf15e6065
A000534
Numbers that are not the sum of 4 nonzero squares.
[ "0", "1", "2", "3", "5", "6", "8", "9", "11", "14", "17", "24", "29", "32", "41", "56", "96", "128", "224", "384", "512", "896", "1536", "2048", "3584", "6144", "8192", "14336", "24576", "32768", "57344", "98304", "131072", "229376", "393216", "5...
[ "nonn", "easy", "nice" ]
63
1
3
[ "A000414", "A000534", "A123069" ]
null
N. J. A. Sloane and J. H. Conway
2024-10-19T15:57:32
oeisdata/seq/A000/A000534.seq
860083b55545690f2a01cd14c7bd37cd
A000535
Card matching: coefficients B[n,2] of t^2 in the reduced hit polynomial A[n,n,n](t).
[ "0", "27", "378", "4536", "48600", "489780", "4738104", "44535456", "409752432", "3708359550", "33125746500", "292779558720", "2565087894720", "22307854940280", "192788833482000", "1657111548654720", "14176605442521312", "120779466450505758", "1025230099571720676", "86742212703...
[ "nonn" ]
30
1
2
[ "A000279", "A000489", "A000535", "A033581" ]
[ "M5194", "N2258" ]
N. J. A. Sloane
2022-02-03T02:30:45
oeisdata/seq/A000/A000535.seq
b7467deb0f118cb319f20c3e4d431af1
A000536
Number of 3-line Latin rectangles.
[ "24", "240", "2520", "26880", "304080", "3671136", "47391120", "653463360", "9603708840", "150046937040", "2485510331304", "43536519673920", "804343214307360", "15636586027419840", "319143375070100640", "6824486562845878656", "152599994618389811640", "3561710724832153990320", "86...
[ "nonn" ]
30
4
1
null
[ "M5152", "N2236" ]
N. J. A. Sloane
2026-01-03T15:45:21
oeisdata/seq/A000/A000536.seq
b8d25bbe3ee23dc4ee1b923a7d385748
A000537
Sum of first n cubes; or n-th triangular number squared.
[ "0", "1", "9", "36", "100", "225", "441", "784", "1296", "2025", "3025", "4356", "6084", "8281", "11025", "14400", "18496", "23409", "29241", "36100", "44100", "53361", "64009", "76176", "90000", "105625", "123201", "142884", "164836", "189225", "216225", ...
[ "nonn", "easy", "nice", "changed" ]
412
0
3
[ "A000217", "A000290", "A000292", "A000330", "A000332", "A000537", "A000538", "A000566", "A000578", "A002415", "A006003", "A008458", "A008459", "A024166", "A035287", "A039623", "A053382", "A053383", "A059376", "A059827", "A059860", "A085582", "A094414", "A094415", "A10...
[ "M4619", "N1972" ]
N. J. A. Sloane
2026-01-05T15:12:37
oeisdata/seq/A000/A000537.seq
bed8243f88fb0e4ddc15273775110e72
A000538
Sum of fourth powers: 0^4 + 1^4 + ... + n^4.
[ "0", "1", "17", "98", "354", "979", "2275", "4676", "8772", "15333", "25333", "39974", "60710", "89271", "127687", "178312", "243848", "327369", "432345", "562666", "722666", "917147", "1151403", "1431244", "1763020", "2153645", "2610621", "3142062", "3756718"...
[ "nonn", "easy", "nice" ]
163
0
3
[ "A000217", "A000330", "A000537", "A000538", "A000539", "A000540", "A000541", "A000542", "A000583", "A007487", "A023002", "A064538", "A101089", "A103438", "A254640" ]
[ "M5043", "N2179" ]
N. J. A. Sloane
2025-09-22T16:00:13
oeisdata/seq/A000/A000538.seq
9dd895a2a0c6de8329c4b506595faf35
A000539
Sum of 5th powers: 0^5 + 1^5 + 2^5 + ... + n^5.
[ "0", "1", "33", "276", "1300", "4425", "12201", "29008", "61776", "120825", "220825", "381876", "630708", "1002001", "1539825", "2299200", "3347776", "4767633", "6657201", "9133300", "12333300", "16417401", "21571033", "28007376", "35970000", "45735625", "57617001...
[ "nonn", "easy" ]
154
0
3
[ "A000217", "A000537", "A000538", "A000539", "A000584", "A006542", "A008292", "A059378", "A101092", "A103438" ]
[ "M5241", "N2280" ]
N. J. A. Sloane
2025-08-21T20:51:44
oeisdata/seq/A000/A000539.seq
eaeaa08554af788f393a5583990e931a
A000540
Sum of 6th powers: 0^6 + 1^6 + 2^6 + ... + n^6.
[ "0", "1", "65", "794", "4890", "20515", "67171", "184820", "446964", "978405", "1978405", "3749966", "6735950", "11562759", "19092295", "30482920", "47260136", "71397705", "105409929", "152455810", "216455810", "302221931", "415601835", "563637724", "754740700", "99...
[ "nonn", "easy" ]
136
0
3
[ "A000539", "A000540", "A001014", "A101093", "A103438" ]
[ "M5335", "N2322" ]
N. J. A. Sloane
2025-09-22T16:00:13
oeisdata/seq/A000/A000540.seq
aef1f80d8264723334647399aaf7bac8
A000541
Sum of 7th powers: 1^7 + 2^7 + ... + n^7.
[ "0", "1", "129", "2316", "18700", "96825", "376761", "1200304", "3297456", "8080425", "18080425", "37567596", "73399404", "136147921", "241561425", "412420800", "680856256", "1091194929", "1703414961", "2597286700", "3877286700", "5678375241", "8172733129", "11577558576...
[ "nonn", "easy" ]
103
0
3
[ "A000217", "A000537", "A000539", "A000541", "A069092", "A103438" ]
[ "M5394", "N2343" ]
N. J. A. Sloane
2025-07-17T09:43:19
oeisdata/seq/A000/A000541.seq
6744e27df266b3e0f5a091065582d54b
A000542
Sum of 8th powers: 1^8 + 2^8 + ... + n^8.
[ "0", "1", "257", "6818", "72354", "462979", "2142595", "7907396", "24684612", "67731333", "167731333", "382090214", "812071910", "1627802631", "3103591687", "5666482312", "9961449608", "16937207049", "27957167625", "44940730666", "70540730666", "108363590027", "1632394635...
[ "nonn", "easy" ]
77
0
3
[ "A000542", "A069093", "A103438" ]
[ "M5427", "N2358" ]
N. J. A. Sloane
2025-09-22T16:00:13
oeisdata/seq/A000/A000542.seq
3d805d5e3bd5612ac9c72b13be8b3f7f
A000543
Number of inequivalent ways to color vertices of a cube using at most n colors.
[ "0", "1", "23", "333", "2916", "16725", "70911", "241913", "701968", "1798281", "4173775", "8942021", "17930628", "34009053", "61518471", "106823025", "179003456", "290715793", "459239463", "707740861", "1066780100", "1576090341", "2286660783", "3263156073", "45867065...
[ "nonn", "easy" ]
44
0
3
[ "A000543", "A000545", "A006008", "A047780", "A054472", "A060530", "A128766", "A325012", "A337891", "A337896", "A337897" ]
null
Clint. C. Williams (Clintwill(AT)aol.com)
2025-02-16T08:32:21
oeisdata/seq/A000/A000543.seq
68debd9605f921a71a2c66e3dd80b6dc
A000544
Number of permutations of length n by rises.
[ "3", "25", "155", "1005", "7488", "64164", "619986", "6646750", "78161249", "999473835", "13801761213", "204631472475", "3241541125110", "54629642149630", "975867376041308", "18416844056075364", "366128842105397631", "7647337600268371485", "167424323805645018159", "383379083403...
[ "nonn" ]
23
4
1
[ "A000544", "A010030" ]
[ "M3110", "N1260" ]
N. J. A. Sloane
2022-02-04T02:01:40
oeisdata/seq/A000/A000544.seq
818d95e58404a8fea1a1d159583eaa29
A000545
Number of ways of n-coloring a dodecahedron.
[ "1", "96", "9099", "280832", "4073375", "36292320", "230719293", "1145393152", "4707296613", "16666924000", "52307593239", "148602435840", "388302646355", "944900450144", "2162441849625", "4691253854208", "9710376716137", "19280531603808", "36888593841475", "68266682784000", ...
[ "nonn", "easy" ]
47
1
2
[ "A000543", "A000545", "A006008", "A047780", "A054472", "A252705", "A282670", "A337961", "A337962" ]
null
Clint. C. Williams (Clintwill(AT)aol.com)
2025-02-16T08:32:21
oeisdata/seq/A000/A000545.seq
9789a5703a5f1cd63a4c7a5fe3893c15
A000546
First occurrence of n consecutive numbers that take same number of steps to reach 1 in 3x+1 problem.
[ "1", "12", "28", "314", "98", "386", "943", "1494", "1680", "4722", "6576", "11696", "3982", "2987", "17548", "36208", "7083", "59692", "159116", "79592", "57857", "212160", "352258", "221185", "57346", "294913", "252548", "530052", "331778", "524289", "10...
[ "nonn" ]
14
1
2
[ "A000546", "A000547" ]
null
Peter L. Stone [ PetStone(AT)aol.com ]
2012-06-20T14:20:41
oeisdata/seq/A000/A000546.seq
7af92715fa8206be0ac23d4334c12554
A000547
Number of steps to reach 1 in sequence A000546.
[ "0", "9", "18", "37", "25", "120", "36", "47", "42", "59", "137", "143", "51", "48", "141", "41", "57", "73", "77", "76", "166", "80", "104", "93", "78", "96", "181", "102", "91", "102", "209", "201", "197", "194", "196", "129", "230", "115",...
[ "nonn" ]
7
1
2
[ "A000546", "A000547" ]
null
Peter L. Stone [ PetStone(AT)aol.com ]
2012-06-20T14:22:23
oeisdata/seq/A000/A000547.seq
b997320dd67a4917da96104359a6b4c6
A000548
Squares that are not the sum of 2 nonzero squares.
[ "1", "4", "9", "16", "36", "49", "64", "81", "121", "144", "196", "256", "324", "361", "441", "484", "529", "576", "729", "784", "961", "1024", "1089", "1296", "1444", "1764", "1849", "1936", "2116", "2209", "2304", "2401", "2916", "3136", "3249", ...
[ "nonn" ]
25
1
2
null
null
N. J. A. Sloane and J. H. Conway
2018-06-20T01:34:15
oeisdata/seq/A000/A000548.seq
7d6d1adf8568d6ae775b3d56831fb214
A000549
Numbers that are the sum of 2 squares but not sum of 3 nonzero squares.
[ "1", "2", "4", "5", "8", "10", "13", "16", "20", "25", "32", "37", "40", "52", "58", "64", "80", "85", "100", "128", "130", "148", "160", "208", "232", "256", "320", "340", "400", "512", "520", "592", "640", "832", "928", "1024", "1280", "136...
[ "nonn" ]
56
1
2
null
null
N. J. A. Sloane and J. H. Conway
2023-10-27T18:23:26
oeisdata/seq/A000/A000549.seq
5d94a45f00d34aebb150995a712ba663
A000550
Number of trees of diameter 7.
[ "1", "3", "14", "42", "128", "334", "850", "2010", "4625", "10201", "21990", "46108", "94912", "191562", "380933", "746338", "1444676", "2763931", "5235309", "9822686", "18275648", "33734658", "61826344", "112550305", "203627610", "366267931", "655261559", "1166...
[ "nonn" ]
34
8
2
[ "A000306", "A000550", "A034853" ]
[ "M2969", "N1201" ]
N. J. A. Sloane
2017-04-03T03:36:54
oeisdata/seq/A000/A000550.seq
a3bafa16ddc979dc4d6c7f439073abd0
A000551
Number of labeled rooted trees of height 2 with n nodes.
[ "6", "36", "200", "1170", "7392", "50568", "372528", "2936070", "24617120", "218521116", "2045278248", "20112821274", "207162957120", "2228888801040", "24989309310944", "291322555295886", "3524580202643136", "44176839081266340", "572725044269255640" ]
[ "nonn", "nice", "easy" ]
41
3
1
null
[ "M4220", "N1764" ]
N. J. A. Sloane
2017-04-17T14:46:36
oeisdata/seq/A000/A000551.seq
d7010e9c23c091436a185b240528d9b0
A000552
Number of labeled rooted trees of height 3 with n nodes.
[ "24", "300", "3360", "38850", "475776", "6231960", "87530400", "1316954430", "21173760960", "362670636900", "6596214691248", "126980000240730", "2579214238608000", "55118036257959600", "1235935135837111104", "29009023670878484598" ]
[ "nonn", "easy", "nice" ]
29
4
1
null
[ "M5159", "N2241" ]
N. J. A. Sloane
2017-04-03T04:23:25
oeisdata/seq/A000/A000552.seq
d6a7c0d86d4015c3e050bf586b2d3c7f
A000553
Number of labeled rooted trees of height 4 with n nodes.
[ "120", "2520", "43680", "757680", "13747104", "264181680", "5395040640", "117080049240", "2696387899920", "65774992411128", "1695845836077120", "46110625382246880", "1319345179723609920", "39640903618873667040", "1248193457738661143808" ]
[ "nonn" ]
31
5
1
null
[ "M5378", "N2335" ]
N. J. A. Sloane
2021-12-19T09:37:24
oeisdata/seq/A000/A000553.seq
589945ea4f7def9acd9184d442f06524
A000554
Number of labeled trees of diameter 3 with n nodes.
[ "12", "60", "210", "630", "1736", "4536", "11430", "28050", "67452", "159588", "372554", "859950", "1965840", "4456176", "10026702", "22412970", "49806980", "110100060", "242220594", "530578950", "1157627352", "2516581800", "5452594550", "11777604930", "25367149836", ...
[ "nonn", "easy" ]
41
4
1
null
[ "M4843", "N2070" ]
N. J. A. Sloane
2017-03-24T00:47:48
oeisdata/seq/A000/A000554.seq
fbea8c70b7c883d6dd7288b03f4d1e60
A000555
Number of labeled trees of diameter 4 with n nodes.
[ "60", "720", "6090", "47040", "363384", "2913120", "24560910", "218386080", "2044958916", "20112075984", "207161237010", "2228884869120", "24989300398320", "291322535242176", "3524580157816854", "44176838981652000", "572725044049055100", "7668896804089696560", "105920137922879314...
[ "nonn" ]
27
5
1
null
[ "M5319", "N2312" ]
N. J. A. Sloane
2016-02-10T03:44:12
oeisdata/seq/A000/A000555.seq
2449390631bb8ee1073d23ed13d282f6
A000556
Expansion of exp(-x) / (1 - exp(x) + exp(-x)).
[ "1", "1", "5", "31", "257", "2671", "33305", "484471", "8054177", "150635551", "3130337705", "71556251911", "1784401334897", "48205833997231", "1402462784186105", "43716593539939351", "1453550100421124417", "51350258701767067711", "1920785418183176050505", "75839622064482770570...
[ "nonn", "easy" ]
91
0
3
[ "A000556", "A005923", "A216794" ]
[ "M3966", "N1638" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A000/A000556.seq
be0d99b70f32874c17fb8e6e24defe90
A000557
Expansion of e.g.f. 1/(1 - 2*sinh(x)).
[ "1", "2", "8", "50", "416", "4322", "53888", "783890", "13031936", "243733442", "5064992768", "115780447730", "2887222009856", "77998677862562", "2269232452763648", "70734934220015570", "2351893466832306176", "83086463910558199682", "3107896091715557654528", "122711086194279627...
[ "nonn", "easy" ]
106
0
2
[ "A000045", "A000556", "A000557", "A005923", "A006154", "A107403", "A136630", "A320352", "A358031", "A358032" ]
[ "M1881", "N0743" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A000/A000557.seq
eae59929c5dfd916bbaf9cf9cc9cf386
A000558
Generalized Stirling numbers of second kind.
[ "1", "6", "32", "175", "1012", "6230", "40819", "283944", "2090424", "16235417", "132609666", "1135846062", "10175352709", "95108406130", "925496853980", "9357279554071", "98118527430960", "1065259283215810", "11956366813630835", "138539436100687988", "1655071323662574756", ...
[ "nonn", "easy" ]
59
2
2
[ "A000110", "A000558", "A000559", "A001861", "A046817", "A130191" ]
[ "M4213", "N1758" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A000/A000558.seq
6d5dee44a1f9fb661996a88b3d5a83ff
A000559
Generalized Stirling numbers of second kind.
[ "1", "12", "110", "945", "8092", "70756", "638423", "5971350", "57996774", "585092607", "6128147610", "66579524648", "749542556193", "8733648533696", "105203108066962", "1308549777461505", "16787682400875456", "221901108871482760", "3018891886411332135", "42230736603244134242" ...
[ "nonn", "easy" ]
41
3
2
[ "A000558", "A000559", "A046817", "A130191" ]
[ "M4858", "N2076" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A000/A000559.seq
d080d5d47a087b3882b8fb60c5da434e
A000560
Number of symmetric ways of folding a strip of n labeled stamps.
[ "1", "2", "5", "12", "33", "87", "252", "703", "2105", "6099", "18689", "55639", "173423", "526937", "1664094", "5137233", "16393315", "51255709", "164951529", "521138861", "1688959630", "5382512216", "17547919924", "56335234064", "184596351277", "596362337295", "...
[ "nonn", "nice" ]
84
2
2
[ "A000136", "A000560", "A000682", "A001011" ]
[ "M1420", "N0557" ]
N. J. A. Sloane, Stéphane Legendre
2025-10-02T16:29:40
oeisdata/seq/A000/A000560.seq
a3a079fb8ce972a0e810a1e471aef4fa
A000561
Number of discordant permutations.
[ "6", "44", "145", "336", "644", "1096", "1719", "2540", "3586", "4884", "6461", "8344", "10560", "13136", "16099", "19476", "23294", "27580", "32361", "37664", "43516", "49944", "56975", "64636", "72954", "81956", "91669", "102120", "113336", "125344", "13...
[ "nonn", "easy" ]
48
3
1
null
[ "M4245", "N1773" ]
N. J. A. Sloane
2025-09-22T16:00:13
oeisdata/seq/A000/A000561.seq
abf2ebab331c71a990791d0c681ef8c1
A000562
Number of discordant permutations.
[ "9", "95", "420", "1225", "2834", "5652", "10165", "16940", "26625", "39949", "57722", "80835", "110260", "147050", "192339", "247342", "313355", "391755", "484000", "591629", "716262", "859600", "1023425", "1209600", "1420069", "1656857", "1922070", "2217895", ...
[ "nonn", "easy" ]
38
4
1
null
[ "M4657", "N1994" ]
N. J. A. Sloane
2022-09-08T08:44:28
oeisdata/seq/A000/A000562.seq
11b763a8227428487d1e5f1f360c97a4
A000563
Number of discordant permutations.
[ "13", "192", "1085", "3880", "10656", "24626", "50380", "94128", "163943", "270004", "424839", "643568", "944146", "1347606", "1878302", "2564152", "3436881", "4532264", "5890369", "7555800", "9577940", "12011194", "14915232", "18355232", "22402123", "27132828", "...
[ "nonn", "easy" ]
38
5
1
null
[ "M4916", "N2109" ]
N. J. A. Sloane
2022-09-08T08:44:28
oeisdata/seq/A000/A000563.seq
ed1ec742d321b19198e132013443313c
A000564
Number of discordant permutations.
[ "20", "371", "2588", "11097", "35645", "94457", "218124", "454220", "872648", "1571715", "2684936", "4388567", "6909867", "10536089", "15624200", "22611330", "32025950", "44499779", "60780420", "81744725", "108412889", "141963273", "183747956", "235309016", "298395540...
[ "nonn", "easy" ]
38
6
1
null
[ "M5099", "N2208" ]
N. J. A. Sloane
2022-09-08T08:44:28
oeisdata/seq/A000/A000564.seq
42749e14f08ca1ca63c73e5e9ac64157
A000565
Number of discordant permutations.
[ "31", "696", "5823", "29380", "108933", "327840", "848380", "1958004", "4130895", "8107024", "14990889", "26372124", "44470165", "72305160", "113897310", "174496828", "260846703", "381480456", "547057075", "770735316", "1068589557", "1460069392", "1968505152", "26216615...
[ "nonn", "easy" ]
38
7
1
null
[ "M5227", "N2275" ]
N. J. A. Sloane
2022-09-08T08:44:28
oeisdata/seq/A000/A000565.seq
7b46020d95867e83b6ac991419463e6c
A000566
Heptagonal numbers (or 7-gonal numbers): n*(5*n-3)/2.
[ "0", "1", "7", "18", "34", "55", "81", "112", "148", "189", "235", "286", "342", "403", "469", "540", "616", "697", "783", "874", "970", "1071", "1177", "1288", "1404", "1525", "1651", "1782", "1918", "2059", "2205", "2356", "2512", "2673", "2839",...
[ "nonn", "easy", "nice", "changed" ]
253
0
3
[ "A000217", "A000326", "A000384", "A000566", "A001622", "A002413", "A005563", "A006564", "A014637", "A014640", "A014773", "A014792", "A069099", "A093562", "A130520", "A131413", "A131896", "A134483", "A147875", "A153126", "A153127", "A244639", "A254963" ]
[ "M4358", "N1826" ]
N. J. A. Sloane
2026-01-08T03:05:53
oeisdata/seq/A000/A000566.seq
b7b13f225f71e472d3be9275eb213567
A000567
Octagonal numbers: n*(3*n-2). Also called star numbers.
[ "0", "1", "8", "21", "40", "65", "96", "133", "176", "225", "280", "341", "408", "481", "560", "645", "736", "833", "936", "1045", "1160", "1281", "1408", "1541", "1680", "1825", "1976", "2133", "2296", "2465", "2640", "2821", "3008", "3201", "3400...
[ "nonn", "easy", "nice" ]
356
0
3
[ "A000217", "A000290", "A000384", "A000567", "A001835", "A002378", "A003154", "A005408", "A014641", "A014642", "A014793", "A014794", "A016777", "A016921", "A045944", "A046092", "A093563" ]
[ "M4493", "N1901" ]
N. J. A. Sloane
2025-11-26T15:59:42
oeisdata/seq/A000/A000567.seq
9ee26de8e9c7e5e2ffc98c879face47d
A000568
Number of outcomes of unlabeled n-team round-robin tournaments.
[ "1", "1", "1", "2", "4", "12", "56", "456", "6880", "191536", "9733056", "903753248", "154108311168", "48542114686912", "28401423719122304", "31021002160355166848", "63530415842308265100288", "244912778438520759443245824", "1783398846284777975419600287232", "2460564117126037677...
[ "nonn", "nice", "easy" ]
118
0
4
[ "A000568", "A006125", "A051337", "A334335" ]
[ "M1262", "N0484" ]
N. J. A. Sloane
2025-11-05T15:21:39
oeisdata/seq/A000/A000568.seq
40271de3132385674c2e870d2c5909f7
A000569
Number of graphical partitions of 2n.
[ "1", "2", "5", "9", "17", "31", "54", "90", "151", "244", "387", "607", "933", "1420", "2136", "3173", "4657", "6799", "9803", "14048", "19956", "28179", "39467", "54996", "76104", "104802", "143481", "195485", "264941", "357635", "480408", "642723", "...
[ "nonn", "nice" ]
81
1
2
[ "A000070", "A000219", "A000569", "A004250", "A004251", "A007717", "A025065", "A029889", "A095268", "A096373", "A147878", "A209816", "A320911", "A320921", "A320922" ]
null
N. J. A. Sloane
2025-04-16T03:03:44
oeisdata/seq/A000/A000569.seq
82cb278e85e897a81a8983d7e54e9bda
A000570
Number of tournaments on n nodes determined by their score vectors.
[ "1", "1", "2", "4", "7", "11", "18", "31", "53", "89", "149", "251", "424", "715", "1204", "2028", "3418", "5761", "9708", "16358", "27565", "46452", "78279", "131910", "222285", "374581", "631222", "1063696", "1792472", "3020560", "5090059", "8577449", ...
[ "nonn", "nice", "easy" ]
39
1
3
null
null
Prasad Tetali [ tetali(AT)math.gatech.edu ]
2025-07-02T16:01:53
oeisdata/seq/A000/A000570.seq
3fce515481a543a81a1bd91b4c673a63
A000571
Number of different score sequences that are possible in an n-team round-robin tournament.
[ "1", "1", "1", "2", "4", "9", "22", "59", "167", "490", "1486", "4639", "14805", "48107", "158808", "531469", "1799659", "6157068", "21258104", "73996100", "259451116", "915695102", "3251073303", "11605141649", "41631194766", "150021775417", "542875459724", "197...
[ "nonn", "nice" ]
153
0
4
[ "A000571", "A007747", "A145855", "A210726", "A274098" ]
[ "M1189", "N0459" ]
N. J. A. Sloane
2025-10-27T11:02:43
oeisdata/seq/A000/A000571.seq
966b47d07e12506dbdb4812683a48d7a
A000572
A Beatty sequence: [ n(e+1) ].
[ "3", "7", "11", "14", "18", "22", "26", "29", "33", "37", "40", "44", "48", "52", "55", "59", "63", "66", "70", "74", "78", "81", "85", "89", "92", "96", "100", "104", "107", "111", "115", "118", "122", "126", "130", "133", "137", "141", "1...
[ "nonn" ]
27
1
1
[ "A000572", "A006594" ]
[ "M2621", "N1037" ]
N. J. A. Sloane
2025-09-12T13:31:55
oeisdata/seq/A000/A000572.seq
51ad9b8b53daf6edbfe246594ef04587
A000573
Number of 4 X n normalized Latin rectangles.
[ "4", "56", "6552", "1293216", "420909504", "207624560256", "147174521059584", "143968880078466048", "188237563987982390784", "320510030393570671051776", "695457005987768649183581184", "1888143905499961681708381310976", "6314083806394358817244705266941952", "25655084790196439186603345691314...
[ "nonn", "nice" ]
27
4
1
[ "A000573", "A001009", "A003170" ]
null
Brendan McKay and Eric Rogoyski
2025-11-18T05:42:26
oeisdata/seq/A000/A000573.seq
1bf08fcea53ddbdc5d36586939846c52
A000574
Coefficient of x^5 in expansion of (1 + x + x^2)^n.
[ "3", "16", "51", "126", "266", "504", "882", "1452", "2277", "3432", "5005", "7098", "9828", "13328", "17748", "23256", "30039", "38304", "48279", "60214", "74382", "91080", "110630", "133380", "159705", "190008", "224721", "264306", "309256", "360096", "4...
[ "nonn", "easy" ]
90
3
1
[ "A000217", "A000389", "A000574", "A005581", "A005712", "A005714", "A005715", "A005716", "A055998", "A095660", "A111808" ]
[ "M3011", "N1219" ]
N. J. A. Sloane
2025-10-21T02:40:03
oeisdata/seq/A000/A000574.seq
9bd0691663495b7a69264eb3505369ad
A000575
Tenth column of quintinomial coefficients.
[ "10", "80", "365", "1246", "3535", "8800", "19855", "41470", "81367", "151580", "270270", "464100", "771290", "1245488", "1960610", "3016820", "4547840", "6729800", "9791859", "14028850", "19816225", "27627600", "38055225", "51833730", "69867525", "93262260", "123...
[ "nonn", "easy" ]
54
0
1
null
[ "M4729", "N2021" ]
N. J. A. Sloane
2023-06-24T21:41:23
oeisdata/seq/A000/A000575.seq
272a25416d01aca2b55c12b30263bb35
A000576
a(n) is the number of (n-2) X n normalized Latin rectangles.
[ "1", "3", "46", "6552", "11270400", "335390189568", "224382967916691456", "4292039421591854273003520", "2905990310033882693113989027594240" ]
[ "nonn", "more" ]
16
3
2
[ "A000576", "A001009" ]
null
Brendan McKay and Eric Rogoyski
2018-11-29T16:00:46
oeisdata/seq/A000/A000576.seq
c4c20ef14a3a6c5a3292a7f3bcc82a0e
A000577
Number of triangular polyominoes (or triangular polyforms, or polyiamonds) with n cells (turning over is allowed, holes are allowed, must be connected along edges).
[ "1", "1", "1", "3", "4", "12", "24", "66", "160", "448", "1186", "3334", "9235", "26166", "73983", "211297", "604107", "1736328", "5000593", "14448984", "41835738", "121419260", "353045291", "1028452717", "3000800627", "8769216722", "25661961898", "75195166667",...
[ "nonn", "hard", "nice" ]
86
1
4
[ "A000105", "A000207", "A000228", "A000577", "A001420", "A006534", "A030223", "A030224", "A070765", "A096361", "A103465" ]
[ "M2374", "N0941" ]
N. J. A. Sloane
2025-11-05T15:21:39
oeisdata/seq/A000/A000577.seq
f69d0638d5eb213141c3516c4db56949
A000578
The cubes: a(n) = n^3.
[ "0", "1", "8", "27", "64", "125", "216", "343", "512", "729", "1000", "1331", "1728", "2197", "2744", "3375", "4096", "4913", "5832", "6859", "8000", "9261", "10648", "12167", "13824", "15625", "17576", "19683", "21952", "24389", "27000", "29791", "327...
[ "nonn", "core", "easy", "nice", "mult" ]
537
0
3
[ "A000292", "A000447", "A000537", "A000578", "A001158", "A003072", "A003325", "A004006", "A004068", "A004126", "A004188", "A004466", "A004467", "A005900", "A006003", "A006527", "A006564", "A006566", "A007412", "A007588", "A024166", "A024670", "A030078", "A048766", "A05...
[ "M4499", "N1905" ]
N. J. A. Sloane
2025-11-05T15:35:22
oeisdata/seq/A000/A000578.seq
c2c77fcf5e7ec01fe69b4c97a4e52009
A000579
Figurate numbers or binomial coefficients C(n,6).
[ "0", "0", "0", "0", "0", "0", "1", "7", "28", "84", "210", "462", "924", "1716", "3003", "5005", "8008", "12376", "18564", "27132", "38760", "54264", "74613", "100947", "134596", "177100", "230230", "296010", "376740", "475020", "593775", "736281", "90...
[ "nonn", "easy", "nice" ]
235
0
8
[ "A000217", "A000292", "A000332", "A000389", "A000579", "A000580", "A000581", "A000582", "A053128", "A053135", "A104712" ]
[ "M4390", "N1847" ]
N. J. A. Sloane
2025-11-28T22:13:37
oeisdata/seq/A000/A000579.seq
0ac249660344cf4371e3cfbade100863
A000580
a(n) = binomial coefficient C(n,7).
[ "1", "8", "36", "120", "330", "792", "1716", "3432", "6435", "11440", "19448", "31824", "50388", "77520", "116280", "170544", "245157", "346104", "480700", "657800", "888030", "1184040", "1560780", "2035800", "2629575", "3365856", "4272048", "5379616", "672452...
[ "nonn", "easy" ]
166
7
2
[ "A000217", "A000292", "A000332", "A000389", "A000579", "A000580", "A000581", "A000582", "A001787", "A053129", "A053136", "A104712", "A242091" ]
[ "M4517", "N1911" ]
N. J. A. Sloane
2025-11-06T12:47:41
oeisdata/seq/A000/A000580.seq
455ec9941a1bb05257e26e9d334fa7ac
A000581
a(n) = binomial coefficient C(n,8).
[ "1", "9", "45", "165", "495", "1287", "3003", "6435", "12870", "24310", "43758", "75582", "125970", "203490", "319770", "490314", "735471", "1081575", "1562275", "2220075", "3108105", "4292145", "5852925", "7888725", "10518300", "13884156", "18156204", "23535820...
[ "nonn", "easy" ]
172
8
2
[ "A000217", "A000292", "A000332", "A000389", "A000579", "A000580", "A000581", "A001787", "A053130", "A053137", "A242091", "A254142" ]
[ "M4626", "N1976" ]
N. J. A. Sloane
2025-11-05T15:35:22
oeisdata/seq/A000/A000581.seq
358c348fcdc63c8224efb676d82e4992
A000582
a(n) = binomial coefficient C(n,9).
[ "1", "10", "55", "220", "715", "2002", "5005", "11440", "24310", "48620", "92378", "167960", "293930", "497420", "817190", "1307504", "2042975", "3124550", "4686825", "6906900", "10015005", "14307150", "20160075", "28048800", "38567100", "52451256", "70607460", ...
[ "easy", "nonn" ]
129
9
2
[ "A000581", "A000582", "A001787", "A035927", "A053131", "A053138", "A242091" ]
[ "M4712", "N2013" ]
N. J. A. Sloane
2025-11-05T15:35:22
oeisdata/seq/A000/A000582.seq
13b7f4999f5d942f4c7aa78f446b6fd2
A000583
Fourth powers: a(n) = n^4.
[ "0", "1", "16", "81", "256", "625", "1296", "2401", "4096", "6561", "10000", "14641", "20736", "28561", "38416", "50625", "65536", "83521", "104976", "130321", "160000", "194481", "234256", "279841", "331776", "390625", "456976", "531441", "614656", "707281"...
[ "nonn", "core", "easy", "nice", "mult" ]
276
0
3
[ "A000290", "A000332", "A000538", "A000583", "A002415", "A002593", "A002646", "A004831", "A005917", "A006008", "A014820", "A039623", "A047928", "A062392", "A071270", "A092181", "A092182", "A092183", "A132366", "A139584", "A187756", "A231303", "A260810", "A267315" ]
[ "M5004", "N2154" ]
N. J. A. Sloane
2025-11-05T15:35:22
oeisdata/seq/A000/A000583.seq
12e0a5a7b2adf5f0c093a90fe8902b0d
A000584
Fifth powers: a(n) = n^5.
[ "0", "1", "32", "243", "1024", "3125", "7776", "16807", "32768", "59049", "100000", "161051", "248832", "371293", "537824", "759375", "1048576", "1419857", "1889568", "2476099", "3200000", "4084101", "5153632", "6436343", "7962624", "9765625", "11881376", "14348...
[ "nonn", "easy", "mult" ]
116
0
3
[ "A000012", "A000290", "A000539", "A000578", "A000583", "A000584", "A001477", "A008292", "A013663", "A022521", "A062392", "A123125", "A162624", "A173018", "A267316" ]
[ "M5231", "N2277" ]
N. J. A. Sloane
2025-10-26T17:09:08
oeisdata/seq/A000/A000584.seq
de3b4fabe1d13ce8c25515bff9884b8e
A000585
Number of equivalence classes of Boolean functions of n variables under GL(n,2).
[ "4", "8", "20", "92", "2744", "950998216", "2076795963681989019155896", "21651217007530946175606768762255421159692845640522169779616" ]
[ "nonn", "easy", "nice" ]
21
1
1
null
[ "M3337", "N1343" ]
N. J. A. Sloane
2020-11-07T10:05:56
oeisdata/seq/A000/A000585.seq
d38e050a29d96dbd3622146db365be1e
A000586
Number of partitions of n into distinct primes.
[ "1", "0", "1", "1", "0", "2", "0", "2", "1", "1", "2", "1", "2", "2", "2", "2", "3", "2", "4", "3", "4", "4", "4", "5", "5", "5", "6", "5", "6", "7", "6", "9", "7", "9", "9", "9", "11", "11", "11", "13", "12", "14", "15", "15", ...
[ "nonn", "nice", "easy" ]
96
0
6
[ "A000009", "A000041", "A000586", "A000607", "A046675", "A070215", "A112022", "A319264", "A319267" ]
[ "M0022", "N0004", "N0039" ]
N. J. A. Sloane
2022-03-27T03:22:41
oeisdata/seq/A000/A000586.seq
761366f889cb485ca7a19481dd156eaa
A000587
Rao Uppuluri-Carpenter numbers (or complementary Bell numbers): e.g.f. = exp(1 - exp(x)).
[ "1", "-1", "0", "1", "1", "-2", "-9", "-9", "50", "267", "413", "-2180", "-17731", "-50533", "110176", "1966797", "9938669", "8638718", "-278475061", "-2540956509", "-9816860358", "27172288399", "725503033401", "5592543175252", "15823587507881", "-168392610536153", ...
[ "sign", "easy", "nice" ]
281
0
6
[ "A000110", "A000587", "A007318", "A011971", "A078937", "A153229", "A213170" ]
[ "M1913", "N0755" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A000/A000587.seq
9b757068779ff2862de5388cc2ea2a2c
A000588
a(n) = 7*binomial(2n,n-3)/(n+4).
[ "0", "0", "0", "1", "7", "35", "154", "637", "2548", "9996", "38760", "149226", "572033", "2187185", "8351070", "31865925", "121580760", "463991880", "1771605360", "6768687870", "25880277150", "99035193894", "379300783092", "1453986335186", "5578559816632", "2142236...
[ "nonn", "easy" ]
123
0
5
[ "A000108", "A000245", "A000344", "A000588", "A001392", "A001622", "A002057", "A003517", "A003518", "A003519", "A009766", "A026014", "A030237", "A033184", "A047072", "A059365", "A099039", "A106566", "A130020" ]
[ "M4413", "N1866" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A000/A000588.seq
0623ec4dafef9852d066a2682775b02f
A000589
a(n) = 11*binomial(2n,n-5)/(n+6).
[ "1", "11", "77", "440", "2244", "10659", "48279", "211508", "904475", "3798795", "15737865", "64512240", "262256280", "1059111900", "4254603804", "17018415216", "67837293986", "269638992062", "1069258071970", "4232010895376", "16723268860760", "65997186039785", "260170725...
[ "nonn", "easy" ]
61
5
2
[ "A000108", "A000589", "A001622", "A214292" ]
[ "M4797", "N2048" ]
N. J. A. Sloane
2025-11-05T15:35:22
oeisdata/seq/A000/A000589.seq
469b00b26c875a3d15978eb85b94999c
A000590
a(n) = 13*binomial(2n,n-6)/(n+7).
[ "1", "13", "104", "663", "3705", "19019", "92092", "427570", "1924065", "8454225", "36463440", "154969620", "650872404", "2707475148", "11173706960", "45812198536", "186803188858", "758201178306", "3065415516592", "12352414499425", "49634247352235", "198954083924505", "79...
[ "nonn", "easy" ]
50
6
2
[ "A000108", "A000590", "A001622", "A214292" ]
[ "M4908", "N2104" ]
N. J. A. Sloane
2025-11-05T15:35:22
oeisdata/seq/A000/A000590.seq
5c54176b1c222ab404afa900f4fb69eb
A000591
Number of n-state 2-input 1-output automata with one initial and one terminal state.
[ "10", "378", "16576", "819470", "45660051", "2846339383", "196946930215", "15006717613499", "1250005718758059", "113076157328915784", "11044120989736000167", "1158658706030435109195", "129976520576914828292552" ]
[ "nonn" ]
16
1
1
null
[ "M4752", "N2033" ]
N. J. A. Sloane
2022-02-01T01:03:49
oeisdata/seq/A000/A000591.seq
a79d2d8b4c6fa294b383deebb322b97f
A000592
Number of nonnegative solutions of x^2 + y^2 = z in first n shells.
[ "1", "3", "4", "6", "8", "9", "11", "13", "15", "17", "19", "20", "22", "26", "28", "30", "31", "33", "35", "37", "39", "41", "43", "45", "48", "50", "52", "54", "56", "58", "62", "64", "65", "67", "69", "71", "73", "75", "79", "81", "8...
[ "nonn", "nice", "easy" ]
34
0
2
[ "A000592", "A000925" ]
[ "M2324", "N0919" ]
N. J. A. Sloane
2023-09-02T04:37:22
oeisdata/seq/A000/A000592.seq
ab8e2a576ee2ead5ef59320a26bacdd1
A000593
Sum of odd divisors of n.
[ "1", "1", "4", "1", "6", "4", "8", "1", "13", "6", "12", "4", "14", "8", "24", "1", "18", "13", "20", "6", "32", "12", "24", "4", "31", "14", "40", "8", "30", "24", "32", "1", "48", "18", "48", "13", "38", "20", "56", "6", "42", "32",...
[ "nonn", "core", "easy", "nice", "mult" ]
293
1
3
[ "A000005", "A000203", "A000265", "A000593", "A001227", "A006128", "A050999", "A051000", "A051001", "A051002", "A065442", "A069289", "A078471", "A247837", "A301799", "A301800" ]
[ "M3197", "N1292" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A000/A000593.seq
58fe8df3217e9947440c67b532f8c50a
A000594
Ramanujan's tau function (or Ramanujan numbers, or tau numbers).
[ "1", "-24", "252", "-1472", "4830", "-6048", "-16744", "84480", "-113643", "-115920", "534612", "-370944", "-577738", "401856", "1217160", "987136", "-6905934", "2727432", "10661420", "-7109760", "-4219488", "-12830688", "18643272", "21288960", "-25499225", "1386571...
[ "sign", "easy", "core", "mult", "nice" ]
421
1
2
[ "A000594", "A004009", "A006352", "A008408", "A010816", "A013973", "A027364", "A037945", "A037946", "A037947", "A037955", "A046694", "A076847", "A098108", "A099059", "A099060", "A106867", "A126812", "A126832", "A262339", "A278577", "A292781" ]
[ "M5153", "N2237" ]
N. J. A. Sloane
2025-11-05T15:21:39
oeisdata/seq/A000/A000594.seq
a3ab6f61762577e5dc05740cfeabf4fa
A000595
Number of binary relations on n unlabeled points.
[ "1", "2", "10", "104", "3044", "291968", "96928992", "112282908928", "458297100061728", "6666621572153927936", "349390545493499839161856", "66603421985078180758538636288", "46557456482586989066031126651104256", "120168591267113007604119117625289606148096", "115205015576047415755389346174...
[ "nonn", "nice" ]
146
0
2
[ "A000088", "A000273", "A000595", "A001173", "A001174", "A002416", "A002724", "A003087", "A003216" ]
[ "M1980", "N0784" ]
N. J. A. Sloane
2025-12-15T11:49:39
oeisdata/seq/A000/A000595.seq
f303b192c199ccc69074e141e31875ac
A000596
Central factorial numbers: A008955(n,2).
[ "4", "49", "273", "1023", "3003", "7462", "16422", "32946", "61446", "108031", "180895", "290745", "451269", "679644", "997084", "1429428", "2007768", "2769117", "3757117", "5022787", "6625311", "8632866", "11123490", "14185990", "17920890", "22441419", "27874539"...
[ "nonn", "easy" ]
104
3
1
[ "A000290", "A000330", "A000596", "A000597", "A008955" ]
[ "M3686", "N1505" ]
N. J. A. Sloane
2025-01-13T10:34:04
oeisdata/seq/A000/A000596.seq
e2eaac1fdedab07a2a458ba9b5486c62
A000597
Central factorial numbers: A008955(n,3).
[ "36", "820", "7645", "44473", "191620", "669188", "1999370", "5293970", "12728936", "28285400", "58856655", "115842675", "217378200", "391367064", "679524340", "1142659012", "1867463260", "2975110060", "4631998657", "7063027565", "10567817084", "15540347900", "22492529150...
[ "nonn", "easy" ]
108
4
1
[ "A000290", "A000330", "A000596", "A000597", "A001303", "A008955" ]
[ "M5255", "N2287" ]
N. J. A. Sloane
2025-01-13T10:46:26
oeisdata/seq/A000/A000597.seq
c21efd420c660da87f0a6aeff5969c6e
A000598
Number of rooted ternary trees with n nodes; number of n-carbon alkyl radicals C(n)H(2n+1) ignoring stereoisomers.
[ "1", "1", "1", "2", "4", "8", "17", "39", "89", "211", "507", "1238", "3057", "7639", "19241", "48865", "124906", "321198", "830219", "2156010", "5622109", "14715813", "38649152", "101821927", "269010485", "712566567", "1891993344", "5034704828", "13425117806"...
[ "nonn", "easy", "nice", "eigen" ]
172
0
4
[ "A000081", "A000598", "A000599", "A000600", "A000602", "A000625", "A000628", "A000678", "A001190", "A010372", "A010373", "A014591", "A032305", "A086194", "A086200", "A261340", "A292553", "A292554", "A292555", "A292556", "A295461", "A298118", "A298120", "A298204", "A29...
[ "M1146", "N0436", "N1341" ]
N. J. A. Sloane
2025-08-19T08:44:30
oeisdata/seq/A000/A000598.seq
5d8ff074e9854622ba33fd9aadc0c2a0
A000599
Number of secondary alcohols (alkanols or alkyl alcohols C_n H_{2n+1} OH) with n carbon atoms.
[ "0", "0", "1", "1", "3", "6", "15", "33", "82", "194", "482", "1188", "2988", "7528", "19181", "49060", "126369", "326863", "849650", "2216862", "5806256", "15256265", "40210657", "106273050", "281593237", "747890675", "1990689459", "5309397294", "14187485959"...
[ "nonn", "easy" ]
32
1
5
[ "A000598", "A000599", "A000600" ]
[ "M2585", "N1023" ]
N. J. A. Sloane
2019-07-05T15:37:10
oeisdata/seq/A000/A000599.seq
50079d9355df9c66951cd48c60073beb
A000600
Number of tertiary alcohols (alkanols or alkyl alcohols C_n H_{2n+1} OH) with n carbon atoms.
[ "0", "0", "0", "0", "1", "1", "3", "7", "17", "40", "102", "249", "631", "1594", "4074", "10443", "26981", "69923", "182158", "476141", "1249237", "3287448", "8677074", "22962118", "60915508", "161962845", "431536102", "1152022025", "3081015684", "8253947104...
[ "nonn", "easy", "nice" ]
34
0
7
[ "A000598", "A000600" ]
[ "M2664", "N1063" ]
N. J. A. Sloane
2019-07-05T15:37:17
oeisdata/seq/A000/A000600.seq
e1637cf479f34675007d445d20fe8fc6