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christopher
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oeis

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2.47k
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666,262,453B
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timestamp
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1999-12-11 03:00:00
2026-01-19 02:46:49
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32
32
A001801
Coefficients of Legendre polynomials.
[ "3", "15", "105", "315", "6930", "18018", "90090", "218790", "2078505", "4849845", "22309287", "50702925", "1825305300", "4071834900", "18032411700", "39671305740", "347123925225", "755505013725", "3273855059475", "7064634602025", "121511715154830", "260382246760350", "11...
[ "nonn" ]
34
0
1
[ "A001790", "A001796", "A001801", "A004733", "A008316", "A011371", "A100258" ]
[ "M3001", "N1216" ]
N. J. A. Sloane
2025-04-26T08:06:29
oeisdata/seq/A001/A001801.seq
c6d4b9fde2530a03e3397c6d3caed483
A001802
Coefficients of Legendre polynomials.
[ "5", "35", "1260", "4620", "30030", "90090", "1021020", "2771340", "14549535", "37182145", "1487285800", "3650610600", "17644617900", "42075627300", "396713057400", "925663800600", "4281195077775", "9821565178425", "178970743251300", "405039050516100", "1822675727322450", "...
[ "nonn" ]
31
0
1
[ "A001796", "A001802", "A011371", "A100258" ]
[ "M3980", "N1649" ]
N. J. A. Sloane
2025-04-26T05:56:21
oeisdata/seq/A001/A001802.seq
a59bd55843e9b9087152574ba6877e66
A001803
Numerators in expansion of (1 - x)^(-3/2).
[ "1", "3", "15", "35", "315", "693", "3003", "6435", "109395", "230945", "969969", "2028117", "16900975", "35102025", "145422675", "300540195", "9917826435", "20419054425", "83945001525", "172308161025", "1412926920405", "2893136075115", "11835556670925" ]
[ "nonn", "frac" ]
116
0
2
[ "A001790", "A001800", "A001803", "A002011", "A002457", "A002596", "A004731", "A004735", "A005430", "A033876", "A046161", "A086116", "A086228", "A100258", "A161198", "A161199", "A161201", "A163590", "A173384", "A173396" ]
[ "M2986", "N1207" ]
N. J. A. Sloane
2025-04-30T16:56:16
oeisdata/seq/A001/A001803.seq
bed4d8fa1c65a226679a2b8547a860ce
A001804
a(n) = n! * C(n,2).
[ "2", "18", "144", "1200", "10800", "105840", "1128960", "13063680", "163296000", "2195424000", "31614105600", "485707622400", "7933224499200", "137305808640000", "2510734786560000", "48373490221056000", "979563176976384000", "20801312169910272000", "462251381553561600000" ]
[ "nonn", "easy" ]
44
2
1
[ "A001804", "A001809", "A120434" ]
[ "M2109", "N0834" ]
N. J. A. Sloane
2021-12-19T10:04:29
oeisdata/seq/A001/A001804.seq
813d3a6b96ab1024399f7c1dc0cdfaf5
A001805
a(n) = n! * binomial(n,3).
[ "6", "96", "1200", "14400", "176400", "2257920", "30481920", "435456000", "6586272000", "105380352000", "1780927948800", "31732897996800", "594991837440000", "11716762337280000", "241867451105280000", "5224336943874048000", "117874102296158208000", "2773508289321369600000" ]
[ "nonn", "easy" ]
45
3
1
[ "A000142", "A000292", "A001113", "A001620", "A001805", "A021012", "A091725", "A099285" ]
[ "M4291", "N1794" ]
N. J. A. Sloane
2025-09-18T15:44:23
oeisdata/seq/A001/A001805.seq
27afb86c4dbf61f120e8793b97d5f8c5
A001806
a(n) = n! * binomial(n,4).
[ "24", "600", "10800", "176400", "2822400", "45722880", "762048000", "13172544000", "237105792000", "4452319872000", "87265469491200", "1784975512320000", "38079477596160000", "846536078868480000", "19591263539527680000", "471496409184632832000", "11787410229615820800000" ]
[ "nonn", "easy" ]
40
4
1
[ "A000142", "A000332", "A001113", "A001620", "A001806", "A021012", "A091725", "A099285" ]
[ "M5165", "N2242" ]
N. J. A. Sloane
2025-09-18T15:44:13
oeisdata/seq/A001/A001806.seq
046587bb6ae6f6012050a8881afdc969
A001807
a(n) = n! * binomial(n,5).
[ "120", "4320", "105840", "2257920", "45722880", "914457600", "18441561600", "379369267200", "8014175769600", "174530938982400", "3926946127104000", "91390746230784000", "2200993805058048000", "54855537910677504000", "1414489227553898496000", "37719712734770626560000" ]
[ "nonn", "easy" ]
42
5
1
[ "A000142", "A000389", "A001113", "A001620", "A001807", "A021012", "A091725", "A099285" ]
[ "M5380", "N2337" ]
N. J. A. Sloane
2025-09-22T16:00:16
oeisdata/seq/A001/A001807.seq
8e6ded4a30a8587508b958e9b7d6d541
A001808
Expansion of 1/((1+x)*(1-x)^12).
[ "1", "11", "67", "297", "1068", "3300", "9076", "22748", "52834", "115126", "237590", "467842", "884236", "1611908", "2845492", "4880668", "8157227", "13316953", "21280337", "33346963", "51325352", "77699128", "115837592", "170260168", "246965732", "353839564", "5...
[ "nonn", "easy" ]
31
0
2
[ "A001808", "A112465" ]
null
N. J. A. Sloane
2025-04-21T10:47:49
oeisdata/seq/A001/A001808.seq
664be75967d3dda03ff5d593cf43cb5e
A001809
a(n) = n! * n(n-1)/4.
[ "0", "0", "1", "9", "72", "600", "5400", "52920", "564480", "6531840", "81648000", "1097712000", "15807052800", "242853811200", "3966612249600", "68652904320000", "1255367393280000", "24186745110528000", "489781588488192000", "10400656084955136000", "231125690776780800000", ...
[ "nonn", "easy", "nice", "eigen" ]
124
0
4
[ "A001620", "A001809", "A008302", "A034968", "A053495", "A064038", "A099285" ]
[ "M4649", "N1989" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001809.seq
bdfa6fc9ebf7e868963b6246460524cf
A001810
a(n) = n!*n*(n-1)*(n-2)/36.
[ "0", "0", "0", "1", "16", "200", "2400", "29400", "376320", "5080320", "72576000", "1097712000", "17563392000", "296821324800", "5288816332800", "99165306240000", "1952793722880000", "40311241850880000", "870722823979008000", "19645683716026368000", "462251381553561600000", ...
[ "nonn" ]
60
0
5
[ "A001113", "A001620", "A001810", "A005130", "A053495", "A091725", "A099285", "A263771" ]
[ "M5019", "N2163" ]
N. J. A. Sloane
2025-09-30T22:23:45
oeisdata/seq/A001/A001810.seq
6014a224ac1ef999e085820579780ee2
A001811
Coefficients of Laguerre polynomials.
[ "1", "25", "450", "7350", "117600", "1905120", "31752000", "548856000", "9879408000", "185513328000", "3636061228800", "74373979680000", "1586644899840000", "35272336619520000", "816302647480320000", "19645683716026368000", "491142092900659200000", "12740803704070041600000" ]
[ "nonn", "easy" ]
43
4
2
[ "A001113", "A001620", "A001811", "A053495", "A091725", "A099285" ]
[ "M5185", "N2253" ]
N. J. A. Sloane
2025-09-22T16:00:16
oeisdata/seq/A001/A001811.seq
26dbb3312fe038f77df57ff9604d9102
A001812
Coefficients of Laguerre polynomials.
[ "1", "36", "882", "18816", "381024", "7620480", "153679680", "3161410560", "66784798080", "1454424491520", "32724551059200", "761589551923200", "18341615042150400", "457129482588979200", "11787410229615820800", "314330939456421888000", "8663746518767628288000", "2466619597107960053...
[ "nonn" ]
50
5
2
[ "A001113", "A001620", "A001812", "A021009", "A091725", "A099285" ]
[ "M5257", "N2289" ]
N. J. A. Sloane
2025-09-22T16:00:16
oeisdata/seq/A001/A001812.seq
d2cd8e97a48da98b650ea1983a31dba1
A001813
Quadruple factorial numbers: a(n) = (2n)!/n!.
[ "1", "2", "12", "120", "1680", "30240", "665280", "17297280", "518918400", "17643225600", "670442572800", "28158588057600", "1295295050649600", "64764752532480000", "3497296636753920000", "202843204931727360000", "12576278705767096320000", "830034394580628357120000", "58102407620...
[ "nonn", "easy", "nice", "changed" ]
311
0
2
[ "A000085", "A000108", "A000142", "A000165", "A000407", "A000680", "A000984", "A001147", "A001700", "A001813", "A006882", "A007696", "A008275", "A008276", "A008545", "A010050", "A037224", "A047055", "A047657", "A048854", "A052714", "A052734", "A059344", "A066325", "A08...
[ "M2040", "N0808" ]
N. J. A. Sloane
2026-01-12T08:48:35
oeisdata/seq/A001/A001813.seq
0f2b32d846dfaab55755a05fe48778a2
A001814
Coefficient of H_2 when expressing x^{2n} in terms of Hermite polynomials H_m.
[ "1", "12", "180", "3360", "75600", "1995840", "60540480", "2075673600", "79394515200", "3352212864000", "154872234316800", "7771770303897600", "420970891461120000", "24481076457277440000", "1521324036987955200000", "100610229646136770560000" ]
[ "nonn", "easy", "changed" ]
77
1
2
[ "A001814", "A001879", "A005430", "A048854", "A067147", "A126804" ]
[ "M4875", "N2088" ]
N. J. A. Sloane
2026-01-12T08:48:30
oeisdata/seq/A001/A001814.seq
bb57f3a9e472d9052530b7aaee3c1680
A001815
a(n) = binomial(n,2) * 2^(n-1).
[ "0", "0", "2", "12", "48", "160", "480", "1344", "3584", "9216", "23040", "56320", "135168", "319488", "745472", "1720320", "3932160", "8912896", "20054016", "44826624", "99614720", "220200960", "484442112", "1061158912", "2315255808", "5033164800", "10905190400",...
[ "nonn", "easy" ]
133
0
3
[ "A001788", "A001793", "A001815", "A055580", "A089264", "A090802" ]
[ "M2021", "N0799" ]
N. J. A. Sloane
2025-12-11T18:04:27
oeisdata/seq/A001/A001815.seq
4a257c7368f4a543fb9f349ca0538907
A001816
Coefficients of x^n in Hermite polynomial H_{n+4}.
[ "12", "120", "720", "3360", "13440", "48384", "161280", "506880", "1520640", "4392960", "12300288", "33546240", "89456640", "233963520", "601620480", "1524105216", "3810263040", "9413591040", "23011000320", "55710842880", "133706022912", "318347673600", "752458137600", ...
[ "nonn", "easy" ]
36
0
1
[ "A001816", "A003472", "A060821" ]
[ "M4862", "N2078" ]
N. J. A. Sloane, Simon Plouffe
2025-07-27T15:06:21
oeisdata/seq/A001/A001816.seq
271c4b7d638da4eb0f4d8970fc14cc14
A001817
G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum_{n>=0} x^(3n+1)/(1-x^(3n+1)).
[ "1", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "2", "2", "2", "1", "3", "1", "1", "2", "3", "2", "2", "1", "2", "2", "2", "1", "4", "1", "2", "2", "3", "1", "2", "2", "2", "2", "2", "2", "4", "1", "2", "2", "3", "1", "...
[ "nonn", "easy" ]
51
1
4
[ "A001620", "A001817", "A001822", "A002324", "A035191", "A051731", "A256425" ]
null
N. J. A. Sloane
2023-11-25T04:44:37
oeisdata/seq/A001/A001817.seq
d3116a9c50dc2ba6e84971e55f8aa0fd
A001818
Squares of double factorials: (1*3*5*...*(2n-1))^2 = ((2*n-1)!!)^2.
[ "1", "1", "9", "225", "11025", "893025", "108056025", "18261468225", "4108830350625", "1187451971330625", "428670161650355625", "189043541287806830625", "100004033341249813400625", "62502520838281133375390625", "45564337691106946230659765625", "38319607998220941779984862890625" ]
[ "nonn", "easy", "nice" ]
163
0
3
[ "A001147", "A001818", "A002454", "A008956", "A012248", "A111595", "A197037" ]
[ "M4669", "N1997" ]
N. J. A. Sloane
2025-11-20T15:44:15
oeisdata/seq/A001/A001818.seq
aa7654c7e5e8259844bb8b0b29556069
A001819
Central factorial numbers: second right-hand column of triangle A008955.
[ "0", "1", "5", "49", "820", "21076", "773136", "38402064", "2483133696", "202759531776", "20407635072000", "2482492033152000", "359072203696128000", "60912644957448192000", "11977654199703478272000", "2702572249389834608640000" ]
[ "nonn", "easy", "nice" ]
80
0
3
[ "A000254", "A001044", "A001819", "A002455", "A007406", "A007407", "A008955", "A024167", "A066989", "A142995", "A162990" ]
[ "M4008", "N1661" ]
N. J. A. Sloane
2020-07-08T20:38:06
oeisdata/seq/A001/A001819.seq
a4e41830a947ddda00192ace22fd7660
A001820
Central factorial numbers: 2nd subdiagonal of A008955.
[ "1", "14", "273", "7645", "296296", "15291640", "1017067024", "84865562640", "8689315795776", "1071814846360896", "156823829909121024", "26862299458337581056", "5325923338791614078976", "1210310405427816646041600", "312542036038910895995289600", "91018216923341770801874534400" ]
[ "nonn" ]
45
0
2
[ "A001820", "A008955", "A049033" ]
[ "M4952", "N2121" ]
N. J. A. Sloane
2025-01-13T10:44:00
oeisdata/seq/A001/A001820.seq
181c9b957fb11f737ab29fbd480a1908
A001821
Central factorial numbers: 3rd subdiagonal of A008955.
[ "1", "30", "1023", "44473", "2475473", "173721912", "15088541896", "1593719752240", "201529405816816", "30092049283982400", "5242380158902146624", "1054368810603158319360", "242558905724502235934976", "63305390270900389045395456", "18607799824329123330114576384" ]
[ "nonn" ]
43
0
2
[ "A001821", "A008955" ]
[ "M5215", "N2269" ]
N. J. A. Sloane
2025-01-13T10:43:02
oeisdata/seq/A001/A001821.seq
9430b8b26f8c4d628db691e7d45f20b4
A001822
Expansion of Sum_{n>=0} x^(3n+2)/(1-x^(3n+2)).
[ "0", "1", "0", "1", "1", "1", "0", "2", "0", "2", "1", "1", "0", "2", "1", "2", "1", "1", "0", "3", "0", "2", "1", "2", "1", "2", "0", "2", "1", "2", "0", "3", "1", "2", "2", "1", "0", "2", "0", "4", "1", "2", "0", "3", "1", "...
[ "nonn", "easy" ]
42
1
8
[ "A000005", "A001620", "A001817", "A001822", "A002324", "A035191", "A256843" ]
null
N. J. A. Sloane
2023-11-25T08:02:02
oeisdata/seq/A001/A001822.seq
2add9ae3ebc709a8793fb760a1883f72
A001823
Central factorial numbers: column 2 in triangle A008956.
[ "0", "9", "259", "1974", "8778", "28743", "77077", "179452", "375972", "725781", "1312311", "2249170", "3686670", "5818995", "8892009", "13211704", "19153288", "27170913", "37808043", "51708462", "69627922", "92446431", "121181181", "157000116", "201236140", "255401...
[ "nonn" ]
47
1
2
[ "A001823", "A008956", "A181888" ]
[ "M4671", "N1998" ]
N. J. A. Sloane
2022-04-13T13:25:16
oeisdata/seq/A001/A001823.seq
bfdc30e22754f4ede10832ae6ca07827
A001824
Central factorial numbers: 1st subdiagonal of A008956.
[ "1", "10", "259", "12916", "1057221", "128816766", "21878089479", "4940831601000", "1432009163039625", "518142759828635250", "228929627246078500875", "121292816354463333793500", "75908014254880833434338125", "55399444912646408707007883750", "46636497509226736668824289999375" ]
[ "nonn", "easy", "nice" ]
55
0
2
[ "A001824", "A001825", "A002455", "A008956", "A049033" ]
[ "M4749", "N2031" ]
N. J. A. Sloane
2025-01-13T10:23:10
oeisdata/seq/A001/A001824.seq
5b030342eb05696d8d91380b45f1bf7a
A001825
Central factorial numbers: 2nd subdiagonal of A008956.
[ "1", "35", "1974", "172810", "21967231", "3841278805", "886165820604", "261042753755556", "95668443268795341", "42707926241367380631", "22821422608929422854674", "14384681946935352617964750", "10562341153570752891930640875" ]
[ "nonn" ]
32
0
2
[ "A001824", "A001825", "A002455", "A008956", "A049033" ]
[ "M5250", "N2284" ]
N. J. A. Sloane
2025-01-13T10:46:38
oeisdata/seq/A001/A001825.seq
9c2b86586839251a829b473bee095f21
A001826
Number of divisors of n of the form 4k+1.
[ "1", "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "1", "1", "3", "2", "2", "1", "2", "2", "1", "1", "2", "2", "2", "2", "2", "1", "2", "2", "2", "2", "1", "1", "4", "...
[ "nonn", "easy" ]
41
1
5
[ "A001227", "A001620", "A001826", "A001842", "A256778" ]
null
N. J. A. Sloane
2025-07-22T15:50:44
oeisdata/seq/A001/A001826.seq
b002d9700ae0ff04760d097dd7a788a7
A001827
Related to graded partially ordered sets.
[ "1", "4", "22", "166", "1726", "24814", "494902", "13729846", "531077086", "28697950174", "2170176736102", "230007989092006", "34211282155446286", "7149766552058591374", "2101690590380890192342", "869808621195903097079446", "507261036269544624540347326" ]
[ "nonn" ]
32
0
2
[ "A000684", "A001827", "A001828", "A001829", "A001830", "A047863", "A361950" ]
[ "M3591", "N1456" ]
N. J. A. Sloane
2023-03-31T14:09:29
oeisdata/seq/A001/A001827.seq
ec3fda9395d729c7ead52819b1b1797f
A001828
Related to graded partially ordered sets.
[ "1", "5", "33", "287", "3309", "50975", "1058493", "29885567", "1156711869", "61815727295", "4589058616413", "475576073939807", "69061902766811229", "14093318360697120095", "4049931601653596366013", "1641314561238334948886207", "939097032426474389539281789" ]
[ "nonn" ]
35
0
2
[ "A000684", "A001827", "A001828", "A001829", "A001830", "A047863", "A361950" ]
[ "M3971", "N1641" ]
N. J. A. Sloane
2023-03-31T14:09:38
oeisdata/seq/A001/A001828.seq
dc227b644a00720fcabe5eae4c8b9807
A001829
Related to graded partially ordered sets.
[ "1", "6", "46", "450", "5650", "91866", "1957066", "55363650", "2109599650", "109773407466", "7894945079386", "792252362302770", "111671194813402930", "22202849561274787866", "6241728810901739517226", "2484011055161613143144610", "1400187830319472451472442690" ]
[ "nonn" ]
34
0
2
[ "A000684", "A001827", "A001828", "A001829", "A001830", "A047863", "A361950" ]
[ "M4252", "N1776" ]
N. J. A. Sloane
2023-03-31T14:09:45
oeisdata/seq/A001/A001829.seq
98e316e045fde01d0226d1932d65240b
A001830
Related to graded partially ordered sets.
[ "1", "7", "61", "661", "8953", "152917", "3334921", "94354981", "3528929353", "177999003157", "12340001650921", "1194005625114661", "162936187792764073", "31536761103831315157", "8677703806537883683081", "3395880602480076153665701", "1889190751946097573211698313" ]
[ "nonn" ]
37
0
2
[ "A000684", "A001827", "A001828", "A001829", "A001830", "A047863", "A361950" ]
[ "M4439", "N1877" ]
N. J. A. Sloane
2024-05-19T08:40:40
oeisdata/seq/A001/A001830.seq
9c6ae305615920ef7312fbaaf8d31b07
A001831
Number of labeled graded partially ordered sets with n elements of height at most 1.
[ "1", "1", "3", "13", "87", "841", "11643", "227893", "6285807", "243593041", "13262556723", "1014466283293", "109128015915207", "16521353903210521", "3524056001906654763", "1059868947134489801413", "449831067019305308555487", "269568708630308018001547681", "2282285405313277784104...
[ "nonn", "nice" ]
64
0
3
[ "A001831", "A001833", "A002031", "A047863", "A048194", "A052296", "A052332", "A135753", "A135754" ]
[ "M2956", "N1194" ]
N. J. A. Sloane
2025-11-14T10:28:37
oeisdata/seq/A001/A001831.seq
e0a991475b1b9732904f5584e86f5230
A001832
Number of labeled connected bipartite graphs on n nodes.
[ "1", "1", "3", "19", "195", "3031", "67263", "2086099", "89224635", "5254054111", "426609529863", "47982981969979", "7507894696005795", "1641072554263066471", "502596525992239961103", "216218525837808950623459", "130887167385831881114006475", "111653218763166828863141636911" ]
[ "nonn", "nice", "easy" ]
63
1
3
[ "A001832", "A002031", "A005142", "A047863", "A047864", "A228861" ]
[ "M3063", "N1241" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001832.seq
1fa57f3febe5ef44ae3d7d658edbcedd
A001833
Number of labeled graded partially ordered sets with n elements.
[ "1", "1", "3", "19", "219", "3991", "106623", "3964339", "199515459", "13399883551", "1197639892983", "143076298623259", "23053861370437659", "5062745845287855271", "1530139311543346178223", "641441466132460086890179", "375107113287994040621904819", "307244526491924695346004951151"...
[ "nonn" ]
41
0
3
[ "A001831", "A001833", "A223911", "A228551", "A361920", "A361951" ]
[ "M3067", "N1243" ]
N. J. A. Sloane
2023-04-01T15:49:02
oeisdata/seq/A001/A001833.seq
5ce7a2fab5717764c67d1f1b6cfed232
A001834
a(0) = 1, a(1) = 5, a(n) = 4*a(n-1) - a(n-2).
[ "1", "5", "19", "71", "265", "989", "3691", "13775", "51409", "191861", "716035", "2672279", "9973081", "37220045", "138907099", "518408351", "1934726305", "7220496869", "26947261171", "100568547815", "375326930089", "1400739172541", "5227629760075", "19509779867759", ...
[ "nonn", "easy", "nice" ]
241
0
2
[ "A001352", "A001353", "A001834", "A001835", "A002531", "A026150", "A049310", "A082841", "A086386", "A094347", "A100047" ]
[ "M3890", "N1598" ]
N. J. A. Sloane
2025-12-20T13:04:49
oeisdata/seq/A001/A001834.seq
49e3f38eaa9aa2c1195341c54cc0a142
A001835
a(n) = 4*a(n-1) - a(n-2), with a(0) = 1, a(1) = 1.
[ "1", "1", "3", "11", "41", "153", "571", "2131", "7953", "29681", "110771", "413403", "1542841", "5757961", "21489003", "80198051", "299303201", "1117014753", "4168755811", "15558008491", "58063278153", "216695104121", "808717138331", "3018173449203", "11263976658481"...
[ "nonn", "easy", "nice", "changed" ]
338
0
3
[ "A001353", "A001519", "A001542", "A001835", "A002530", "A003699", "A005246", "A006253", "A048788", "A052530", "A079935", "A082841", "A096147", "A099390", "A101265", "A103997", "A125077" ]
[ "M2894", "N1160" ]
N. J. A. Sloane
2026-01-09T10:01:36
oeisdata/seq/A001/A001835.seq
67c1dd4b3d9349059f9129d9ca29835d
A001836
Numbers k such that phi(2k-1) < phi(2k), where phi is Euler's totient function A000010.
[ "53", "83", "158", "263", "293", "368", "578", "683", "743", "788", "878", "893", "908", "998", "1073", "1103", "1208", "1238", "1268", "1403", "1418", "1502", "1523", "1658", "1733", "1838", "1943", "1964", "2048", "2063", "2153", "2228", "2243", "2...
[ "nonn", "nice" ]
50
1
1
[ "A000010", "A001836", "A001837" ]
[ "M5429", "N2359" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001836.seq
7936d5a18068ed1e12ca329947965f9e
A001837
Numbers k such that phi(2k+1) < phi(2k).
[ "157", "262", "367", "412", "472", "487", "577", "682", "787", "877", "892", "907", "997", "1072", "1207", "1237", "1312", "1402", "1522", "1567", "1627", "1657", "1732", "1852", "1942", "2047", "2062", "2152", "2194", "2257", "2362", "2437", "2467", ...
[ "nonn" ]
32
1
1
[ "A000010", "A001837" ]
[ "M5406", "N2349" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001837.seq
b1e2bb72d7c0e5117dd2f9105cdaaa5b
A001838
Numbers k such that phi(k+2) = phi(k) + 2.
[ "3", "5", "6", "11", "12", "14", "17", "18", "20", "29", "41", "44", "59", "62", "71", "92", "101", "107", "116", "137", "149", "164", "179", "191", "197", "212", "227", "239", "254", "269", "281", "311", "332", "347", "356", "419", "431", "4...
[ "nonn", "nice" ]
53
1
1
[ "A001838", "A050472", "A050473", "A056853" ]
[ "M2397", "N0951" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001838.seq
a7bcb3871fe981cb30b677c430407eef
A001839
The coding-theoretic function A(n,4,3).
[ "0", "0", "1", "1", "2", "4", "7", "8", "12", "13", "17", "20", "26", "28", "35", "37", "44", "48", "57", "60", "70", "73", "83", "88", "100", "104", "117", "121", "134", "140", "155", "160", "176", "181", "197", "204", "222", "228", "247",...
[ "nonn", "easy", "nice" ]
75
1
5
[ "A001839", "A001843", "A011975", "A060407" ]
[ "M1032", "N0389" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001839.seq
7ac1b9e39b515f16e34c554cd585d26c
A001840
Expansion of g.f. x/((1 - x)^2*(1 - x^3)).
[ "0", "1", "2", "3", "5", "7", "9", "12", "15", "18", "22", "26", "30", "35", "40", "45", "51", "57", "63", "70", "77", "84", "92", "100", "108", "117", "126", "135", "145", "155", "165", "176", "187", "198", "210", "222", "234", "247", "260...
[ "nonn", "easy", "nice" ]
241
0
3
[ "A000031", "A000217", "A001037", "A001318", "A001399", "A001840", "A007052", "A007304", "A008748", "A011782", "A011847", "A014311", "A014612", "A045943", "A051168", "A058937", "A069905", "A130205", "A156040", "A218004", "A258708", "A337453", "A337483", "A337484" ]
[ "M0638", "N0233" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001840.seq
04fdb95a40e7cd3c2ef5813313cb4bd7
A001841
Related to Zarankiewicz's problem.
[ "3", "5", "10", "14", "21", "26", "36", "43", "55", "64", "78", "88", "105", "117", "136", "150", "171", "186", "210", "227", "253", "272", "300", "320", "351", "373", "406", "430", "465", "490", "528", "555", "595", "624", "666", "696", "741",...
[ "nonn" ]
40
3
1
null
[ "M2460", "N0977" ]
N. J. A. Sloane
2025-11-09T21:21:11
oeisdata/seq/A001/A001841.seq
f00aabc2142105146b7b70ddf178837e
A001842
Expansion of Sum_{n>=0} x^(4*n+3)/(1 - x^(4*n+3)).
[ "0", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "1", "2", "0", "0", "1", "1", "0", "2", "1", "1", "1", "0", "0", "2", "1", "0", "2", "1", "0", "2", "0", "2", "1", "0", "1", "2", "0", "0", "2", "1", "1", "...
[ "nonn", "easy" ]
53
0
16
[ "A001227", "A001620", "A001826", "A001842", "A072437", "A256846" ]
null
N. J. A. Sloane
2025-07-22T15:50:40
oeisdata/seq/A001/A001842.seq
5c3ca4177b465521a467567c421e7a23
A001843
The coding-theoretic function A(n,4,4).
[ "1", "1", "3", "7", "14", "18", "30", "35", "51", "65", "91", "105", "140", "157", "198", "228", "285", "315", "385", "419", "498", "550", "650", "702", "819", "877", "1005", "1085", "1240", "1320", "1496", "1583", "1773", "1887", "2109", "2223",...
[ "nonn", "nice", "easy" ]
43
4
3
null
[ "M2644", "N1052" ]
N. J. A. Sloane
2022-09-25T07:19:28
oeisdata/seq/A001/A001843.seq
738c86ca4ae4c237761a6b1aae13eeb4
A001844
Centered square numbers: a(n) = 2*n*(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z=Y+1) ordered by increasing Z; then sequence gives Z values.
[ "1", "5", "13", "25", "41", "61", "85", "113", "145", "181", "221", "265", "313", "365", "421", "481", "545", "613", "685", "761", "841", "925", "1013", "1105", "1201", "1301", "1405", "1513", "1625", "1741", "1861", "1985", "2113", "2245", "2381",...
[ "nonn", "easy", "nice" ]
631
0
2
[ "A000217", "A000290", "A000982", "A001263", "A001788", "A001844", "A001845", "A002061", "A002144", "A003215", "A004431", "A005408", "A005448", "A005891", "A005900", "A005917", "A008288", "A008586", "A008844", "A016754", "A027862", "A046092", "A048395", "A051890", "A05...
[ "M3826", "N1567" ]
N. J. A. Sloane
2025-12-11T16:29:30
oeisdata/seq/A001/A001844.seq
fa295c15a51bc64bc34e319c67e51c9b
A001845
Centered octahedral numbers (crystal ball sequence for cubic lattice).
[ "1", "7", "25", "63", "129", "231", "377", "575", "833", "1159", "1561", "2047", "2625", "3303", "4089", "4991", "6017", "7175", "8473", "9919", "11521", "13287", "15225", "17343", "19649", "22151", "24857", "27775", "30913", "34279", "37881", "41727", ...
[ "nonn", "easy", "nice" ]
196
0
2
[ "A001845", "A001846", "A001847", "A001848", "A002412", "A005893", "A005894", "A005897", "A005898", "A005899", "A005901", "A005902", "A005917", "A007202", "A007899", "A008137", "A008288", "A008412", "A010001", "A013609", "A014820", "A016061", "A049480", "A057813", "A06...
[ "M4384", "N1844" ]
N. J. A. Sloane
2025-10-25T05:11:46
oeisdata/seq/A001/A001845.seq
9226e0441d7f96198001fd0a0fcafd84
A001846
Centered 4-dimensional orthoplex numbers (crystal ball sequence for 4-dimensional cubic lattice).
[ "1", "9", "41", "129", "321", "681", "1289", "2241", "3649", "5641", "8361", "11969", "16641", "22569", "29961", "39041", "50049", "63241", "78889", "97281", "118721", "143529", "172041", "204609", "241601", "283401", "330409", "383041", "441729", "506921", ...
[ "nonn", "easy" ]
124
0
2
[ "A001844", "A001845", "A001846", "A001847", "A005408", "A008288", "A008412", "A013609", "A059100", "A240876" ]
[ "M4622", "N1974" ]
N. J. A. Sloane
2025-12-15T09:03:10
oeisdata/seq/A001/A001846.seq
9112637511d45e33a93ef5876f54e834
A001847
Crystal ball sequence for 5-dimensional cubic lattice.
[ "1", "11", "61", "231", "681", "1683", "3653", "7183", "13073", "22363", "36365", "56695", "85305", "124515", "177045", "246047", "335137", "448427", "590557", "766727", "982729", "1244979", "1560549", "1937199", "2383409", "2908411", "3522221", "4235671", "50...
[ "nonn", "easy" ]
90
0
2
[ "A001844", "A001845", "A001846", "A001847", "A005408", "A008288", "A013609", "A240876" ]
[ "M4793", "N2045" ]
N. J. A. Sloane
2025-10-30T12:17:35
oeisdata/seq/A001/A001847.seq
d50f950c087084c5142c3d25777ebd05
A001848
Crystal ball sequence for 6-dimensional cubic lattice.
[ "1", "13", "85", "377", "1289", "3653", "8989", "19825", "40081", "75517", "134245", "227305", "369305", "579125", "880685", "1303777", "1884961", "2668525", "3707509", "5064793", "6814249", "9041957", "11847485", "15345233", "19665841", "24957661", "31388293", ...
[ "nonn", "easy" ]
76
0
2
[ "A001847", "A001848", "A008288", "A013609", "A240876" ]
[ "M4904", "N2102" ]
N. J. A. Sloane
2025-12-15T09:05:56
oeisdata/seq/A001/A001848.seq
76ed76f86b94179f740e119880bf71b4
A001849
Crystal ball sequence for 7-dimensional cubic lattice.
[ "1", "15", "113", "575", "2241", "7183", "19825", "48639", "108545", "224143", "433905", "795455", "1392065", "2340495", "3800305", "5984767", "9173505", "13726991", "20103025", "28875327", "40754369", "56610575", "77500017", "104692735", "139703809", "184327311", ...
[ "nonn", "easy" ]
59
0
2
[ "A001848", "A001849", "A008288", "A240876" ]
[ "M4979", "N2139" ]
N. J. A. Sloane
2024-03-23T08:17:10
oeisdata/seq/A001/A001849.seq
a6cf108948942a1b3b8ef075ca94c8ab
A001850
Central Delannoy numbers: a(n) = Sum_{k=0..n} C(n,k)*C(n+k,k).
[ "1", "3", "13", "63", "321", "1683", "8989", "48639", "265729", "1462563", "8097453", "45046719", "251595969", "1409933619", "7923848253", "44642381823", "252055236609", "1425834724419", "8079317057869", "45849429914943", "260543813797441", "1482376214227923", "8443414161...
[ "nonn", "easy", "nice", "changed" ]
513
0
2
[ "A000129", "A001850", "A008288", "A026003", "A027618", "A047665", "A052141", "A064861", "A078057", "A084773", "A109980", "A152250", "A241023", "A243949", "A262809", "A263159" ]
[ "M2942", "N1184" ]
N. J. A. Sloane
2026-01-05T12:44:19
oeisdata/seq/A001/A001850.seq
ff362c86fa53c7ddebc5c38a6af8f9ac
A001851
Total diameter of unlabeled trees with n nodes.
[ "0", "1", "2", "5", "9", "21", "44", "103", "232", "571", "1368", "3441", "8653", "22263", "57518", "150733", "396937", "1054540", "2815453", "7562159", "20399714", "55280532", "150356806", "410432671", "1123902587", "3086827578", "8500975970", "23470712241", ...
[ "nonn" ]
29
1
3
null
[ "M1363", "N0527" ]
N. J. A. Sloane
2025-11-10T21:50:37
oeisdata/seq/A001/A001851.seq
30648cd8ab1100defef0f3455c47cb19
A001852
Total diameter of labeled trees with n nodes.
[ "0", "1", "6", "44", "430", "5322", "79184", "1381144", "27730602", "630422390", "16006336852", "448982630340", "13792542282974", "460632431511826", "16620059192605080", "644338908974954672", "26713929408696716242", "1179487563859389821166" ]
[ "nonn" ]
26
1
3
[ "A001852", "A034854" ]
[ "M4247", "N1774" ]
N. J. A. Sloane
2022-02-04T00:47:04
oeisdata/seq/A001/A001852.seq
b85718234c7ce143964906c92794de04
A001853
Total height of trees with n nodes.
[ "0", "1", "3", "8", "22", "58", "158", "425", "1161", "3175", "8751", "24192", "67239", "187459", "524579", "1472086", "4142639", "11685501", "33036492", "93583873", "265589158", "754998424", "2149588878", "6128914829", "17497927510", "50017546412", "143137957590"...
[ "nonn" ]
27
1
3
[ "A001853", "A034781" ]
[ "M2743", "N1102" ]
N. J. A. Sloane
2022-02-04T00:46:55
oeisdata/seq/A001/A001853.seq
317121768e98eeb0136d2f6292eb24e9
A001854
Total height of all rooted trees on n labeled nodes.
[ "0", "2", "15", "148", "1785", "26106", "449701", "8927192", "200847681", "5053782070", "140679853941", "4293235236324", "142553671807729", "5116962926162738", "197459475792232725", "8152354312656732976", "358585728464893234305", "16741214317684425260142", "8268424577273068031109...
[ "nonn" ]
47
1
2
[ "A000435", "A001854", "A034855", "A234953", "A236396" ]
[ "M2081", "N0822" ]
N. J. A. Sloane
2022-06-21T19:56:06
oeisdata/seq/A001/A001854.seq
fe15d16d112712735b6eb2007d3f7710
A001855
Sorting numbers: maximal number of comparisons for sorting n elements by binary insertion.
[ "0", "1", "3", "5", "8", "11", "14", "17", "21", "25", "29", "33", "37", "41", "45", "49", "54", "59", "64", "69", "74", "79", "84", "89", "94", "99", "104", "109", "114", "119", "124", "129", "135", "141", "147", "153", "159", "165", "171"...
[ "nonn", "easy", "nice" ]
126
1
3
[ "A000337", "A001855", "A003071", "A029837", "A030190", "A030308", "A061168", "A123753", "A373709" ]
[ "M2433", "N0963" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001855.seq
9d5f9eb5567ad27ae5adba0aa0eab00c
A001856
A self-generating sequence: every positive integer occurs as a(i)-a(j) for a unique pair i,j.
[ "1", "2", "4", "8", "16", "21", "42", "51", "102", "112", "224", "235", "470", "486", "972", "990", "1980", "2002", "4004", "4027", "8054", "8078", "16156", "16181", "32362", "32389", "64778", "64806", "129612", "129641", "259282", "259313", "518626", ...
[ "nonn", "easy", "nice" ]
50
1
2
[ "A001856", "A004978", "A054540", "A247556" ]
[ "M1112", "N0425" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001856.seq
76b66017fb7ed3409ea0ae689fe51c81
A001857
a(1)=2, a(2)=3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < n.
[ "2", "3", "5", "7", "8", "9", "13", "14", "18", "19", "24", "25", "29", "30", "35", "36", "40", "41", "46", "51", "56", "63", "68", "72", "73", "78", "79", "83", "84", "89", "94", "115", "117", "126", "153", "160", "165", "169", "170", "1...
[ "nonn", "nice" ]
54
1
1
[ "A001857", "A100729", "A199122", "A199123" ]
[ "M0634", "N0231" ]
N. J. A. Sloane
2025-11-15T07:02:22
oeisdata/seq/A001/A001857.seq
7855d46289576277c1b45954c2b06c50
A001858
Number of forests of trees on n labeled nodes.
[ "1", "1", "2", "7", "38", "291", "2932", "36961", "561948", "10026505", "205608536", "4767440679", "123373203208", "3525630110107", "110284283006640", "3748357699560961", "137557910094840848", "5421179050350334929", "228359487335194570528", "10239206473040881277575", "4869097...
[ "nonn", "easy", "eigen" ]
132
0
3
[ "A000055", "A000088", "A000169", "A000272", "A001858", "A002494", "A002807", "A005195", "A006125", "A006129", "A006572", "A006573", "A053530", "A054548", "A088956", "A105784", "A137916", "A138464", "A144958", "A213434", "A263340", "A322661", "A367863", "A372168", "A37...
[ "M1804", "N0714" ]
N. J. A. Sloane and Simon Plouffe
2025-11-03T13:12:55
oeisdata/seq/A001/A001858.seq
57a2de4f0161c5b2f10124fb697c8749
A001859
Triangular numbers plus quarter-squares: n*(n+1)/2 + floor((n+1)^2/4) (i.e., A000217(n) + A002620(n+1)).
[ "0", "2", "5", "10", "16", "24", "33", "44", "56", "70", "85", "102", "120", "140", "161", "184", "208", "234", "261", "290", "320", "352", "385", "420", "456", "494", "533", "574", "616", "660", "705", "752", "800", "850", "901", "954", "1008"...
[ "nonn", "easy", "nice" ]
100
0
2
[ "A000217", "A001859", "A002378", "A002620", "A003984", "A004526", "A006578", "A045944", "A045947", "A049450", "A077043", "A107661", "A185212" ]
[ "M1368", "N0531" ]
N. J. A. Sloane
2026-01-04T00:48:42
oeisdata/seq/A001/A001859.seq
19940f41f42e10dfa76ef3a93e8a9624
A001860
Number of series-reduced planted trees with n+9 nodes and 4 internal nodes.
[ "0", "3", "12", "29", "57", "99", "157", "234", "333", "456", "606", "786", "998", "1245", "1530", "1855", "2223", "2637", "3099", "3612", "4179", "4802", "5484", "6228", "7036", "7911", "8856", "9873", "10965", "12135", "13385", "14718", "16137", "1...
[ "nonn" ]
34
0
2
null
[ "M2917", "N1171" ]
N. J. A. Sloane
2023-06-25T02:44:31
oeisdata/seq/A001/A001860.seq
97cbf1d3ab772eed27b1a1e52723abae
A001861
Expansion of e.g.f. exp(2*(exp(x) - 1)).
[ "1", "2", "6", "22", "94", "454", "2430", "14214", "89918", "610182", "4412798", "33827974", "273646526", "2326980998", "20732504062", "192982729350", "1871953992254", "18880288847750", "197601208474238", "2142184050841734", "24016181943732414", "278028611833689478", "331...
[ "nonn", "easy", "nice" ]
225
0
2
[ "A000110", "A000587", "A001861", "A002871", "A027710", "A033306", "A035009", "A036073", "A049020", "A056857", "A068199", "A068200", "A068201", "A078937", "A078938", "A078944", "A078945", "A109128", "A129323", "A129324", "A129325", "A129327", "A129328", "A129329", "A12...
[ "M1662", "N0653" ]
N. J. A. Sloane, Simon Plouffe
2025-11-10T21:50:37
oeisdata/seq/A001/A001861.seq
b0fc54149ccc18c43759b0ecf550b924
A001862
Number of forests of least height with n nodes.
[ "1", "1", "2", "7", "26", "111", "562", "3151", "19252", "128449", "925226", "7125009", "58399156", "507222535", "4647051970", "44747776651", "451520086208", "4761032807937", "52332895618066", "598351410294193", "7102331902602676", "87365859333294151", "111194194673868252...
[ "nonn" ]
38
0
3
[ "A000085", "A000169", "A000272", "A000666", "A001862", "A002494", "A003465", "A006125", "A006129", "A053530", "A054548", "A062740", "A066383", "A133686", "A322661", "A322700", "A368597", "A369191", "A369199" ]
[ "M1773", "N0702" ]
N. J. A. Sloane
2024-05-19T14:02:59
oeisdata/seq/A001/A001862.seq
9549acf66ee08b93ba0a07dfd99da0fb
A001863
Normalized total height of rooted trees with n nodes.
[ "0", "1", "4", "26", "236", "2760", "39572", "672592", "13227804", "295579520", "7398318500", "205075286784", "6236796259916", "206489747516416", "7393749269685300", "284714599444490240", "11733037015160276348", "515240326393584058368", "24019843795708471562564", "1184776250223...
[ "nonn", "nice", "easy" ]
86
1
3
[ "A000169", "A000435", "A001863", "A001864" ]
[ "M3614", "N1466" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001863.seq
a0fd20867dd9e1c16743794f0237ab73
A001864
Total height of rooted trees with n labeled nodes.
[ "0", "2", "24", "312", "4720", "82800", "1662024", "37665152", "952401888", "26602156800", "813815035000", "27069937855488", "972940216546896", "37581134047987712", "1552687346633913000", "68331503866677657600", "3191386068123595166656", "157663539876436721860608" ]
[ "nonn", "easy", "nice" ]
85
1
2
[ "A000435", "A001863", "A001864" ]
[ "M2138", "N0850" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001864.seq
2b73b7df41616242a5ceaefe4e066bcc
A001865
Number of connected functions on n labeled nodes.
[ "1", "3", "17", "142", "1569", "21576", "355081", "6805296", "148869153", "3660215680", "99920609601", "2998836525312", "98139640241473", "3478081490967552", "132705415800984825", "5423640496274200576", "236389784118231290049", "10944997108429625524224", "536484538620663729658993...
[ "nonn", "easy", "nice", "changed" ]
157
1
2
[ "A000435", "A001865", "A060281", "A063169" ]
[ "M3040", "N1232" ]
N. J. A. Sloane
2026-01-16T13:16:52
oeisdata/seq/A001/A001865.seq
a3e8838990afdf7240a8df638e163471
A001866
Number of connected graphs with n nodes and n edges.
[ "0", "0", "1", "24", "936", "56640", "4968000", "598328640", "94916183040", "19200422062080", "4826695329792000", "1476585999504000000", "540272647694971699200", "233019960215154829516800", "117009251702203840384204800", "67680314823703303654732800000", "44677678066673631080900198400...
[ "nonn" ]
29
0
4
[ "A001866", "A174586" ]
[ "M5170", "N2245" ]
N. J. A. Sloane
2024-12-27T03:49:24
oeisdata/seq/A001/A001866.seq
f6c55bdddb274b4746db47422929ebd7
A001867
Number of n-bead necklaces with 3 colors.
[ "1", "3", "6", "11", "24", "51", "130", "315", "834", "2195", "5934", "16107", "44368", "122643", "341802", "956635", "2690844", "7596483", "21524542", "61171659", "174342216", "498112275", "1426419858", "4093181691", "11767920118", "33891544419", "97764131646", ...
[ "nonn", "easy", "nice" ]
91
0
2
[ "A001867", "A054610", "A075195" ]
[ "M2548", "N1008" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001867.seq
7de4739b27095901fc3b01b4002951e4
A001868
Number of n-bead necklaces with 4 colors.
[ "1", "4", "10", "24", "70", "208", "700", "2344", "8230", "29144", "104968", "381304", "1398500", "5162224", "19175140", "71582944", "268439590", "1010580544", "3817763740", "14467258264", "54975633976", "209430787824", "799645010860", "3059510616424", "11728124734500...
[ "nonn", "nice", "easy" ]
87
0
2
[ "A001868", "A054611", "A075195" ]
[ "M3390", "N1370" ]
N. J. A. Sloane
2025-01-03T12:29:53
oeisdata/seq/A001/A001868.seq
7e2313701af113b98fa08856f3e88cdd
A001869
Number of n-bead necklaces with 5 colors.
[ "1", "5", "15", "45", "165", "629", "2635", "11165", "48915", "217045", "976887", "4438925", "20346485", "93900245", "435970995", "2034505661", "9536767665", "44878791365", "211927736135", "1003867701485", "4768372070757", "22706531350485", "108372083629275", "518301258...
[ "nonn", "easy" ]
76
0
2
[ "A001869", "A054612", "A075195" ]
[ "M3860", "N1582" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001869.seq
ad496ce16730e0fbdfdef7089ef25fad
A001870
Expansion of (1-x)/(1 - 3*x + x^2)^2.
[ "1", "5", "19", "65", "210", "654", "1985", "5911", "17345", "50305", "144516", "411900", "1166209", "3283145", "9197455", "25655489", "71293590", "197452746", "545222465", "1501460635", "4124739581", "11306252545", "30928921224", "84451726200", "230204999425" ]
[ "nonn", "easy" ]
119
0
2
[ "A001870", "A001871", "A023610", "A030267", "A060921", "A121466" ]
[ "M3886", "N1595" ]
N. J. A. Sloane
2025-09-22T16:00:16
oeisdata/seq/A001/A001870.seq
7b606d1457d988f16a3d92ed2702899e
A001871
Expansion of 1/(1 - 3*x + x^2)^2.
[ "1", "6", "25", "90", "300", "954", "2939", "8850", "26195", "76500", "221016", "632916", "1799125", "5082270", "14279725", "39935214", "111228804", "308681550", "853904015", "2355364650", "6480104231", "17786356776", "48715278000", "133167004200", "363372003625", "...
[ "nonn", "easy" ]
162
0
2
[ "A000045", "A000051", "A001629", "A001820", "A001870", "A001871", "A001906", "A002720", "A049310", "A238846" ]
[ "M4166", "N1733" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001871.seq
7cbede0309eb3d73f303db7ad1160f31
A001872
Convolved Fibonacci numbers.
[ "1", "4", "14", "40", "105", "256", "594", "1324", "2860", "6020", "12402", "25088", "49963", "98160", "190570", "366108", "696787", "1315072", "2463300", "4582600", "8472280", "15574520", "28481220", "51833600", "93914325", "169457708", "304597382", "545556512"...
[ "nonn", "easy" ]
102
0
2
null
[ "M3476", "N1413" ]
N. J. A. Sloane and Simon Plouffe
2025-11-26T15:59:31
oeisdata/seq/A001/A001872.seq
5dcc191287d69f28e72fcc24205ff5ae
A001873
Convolved Fibonacci numbers.
[ "1", "5", "20", "65", "190", "511", "1295", "3130", "7285", "16435", "36122", "77645", "163730", "339535", "693835", "1399478", "2790100", "5504650", "10758050", "20845300", "40075630", "76495450", "145052300", "273381350", "512347975", "955187033", "1772132390", ...
[ "nonn" ]
64
0
2
null
[ "M3899", "N1600" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001873.seq
50d82e86e4e40af3df981ef3ffdf62a1
A001874
Convolved Fibonacci numbers.
[ "1", "6", "27", "98", "315", "924", "2534", "6588", "16407", "39430", "91959", "209034", "464723", "1013292", "2171850", "4584620", "9546570", "19635840", "39940460", "80421600", "160437690", "317354740", "622844730", "1213580820", "2348773525", "4517541378", "863...
[ "nonn", "easy" ]
55
0
2
[ "A001874", "A049310" ]
[ "M4174", "N1738" ]
N. J. A. Sloane, Simon Plouffe
2025-11-02T16:31:05
oeisdata/seq/A001/A001874.seq
1830d4256f22e08e4f635fc4c4df2188
A001875
Convolved Fibonacci numbers.
[ "1", "7", "35", "140", "490", "1554", "4578", "12720", "33705", "85855", "211519", "506408", "1182650", "2702350", "6056850", "13343820", "28947240", "61926900", "130814600", "273163100", "564415390", "1154933230", "2342193350", "4710707400", "9401674275", "18629923...
[ "nonn" ]
52
0
2
null
[ "M4412", "N1865" ]
N. J. A. Sloane, Simon Plouffe
2023-08-05T16:53:28
oeisdata/seq/A001/A001875.seq
c6c5915e78431e25d83bf69942ed67fc
A001876
Number of divisors of n of the form 5k+1; a(0)=0.
[ "0", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "1", "1", "1", "2", "1", "2", "1", "1", "2", "2", "1", "2", "1", "2", "1", "1", "1", "2", "2", "2", "2", "1", "1", "3", "1", "1", "1", "1", "2", "3", "1", "2", "...
[ "nonn", "easy" ]
38
0
7
[ "A001620", "A001876", "A001877", "A001878", "A001899", "A256779" ]
null
N. J. A. Sloane
2023-11-25T04:34:26
oeisdata/seq/A001/A001876.seq
aa0a30333036db1141bbe35555fa5e68
A001877
Number of divisors of n of the form 5k+2; a(0) = 0.
[ "0", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "2", "0", "2", "0", "1", "1", "1", "0", "1", "1", "2", "0", "2", "0", "1", "1", "2", "0", "1", "0", "2", "0", "2", "1", "2", "1", "1", "0", "1", "0", "3", "0", "2", "...
[ "nonn", "easy" ]
29
0
13
[ "A001620", "A001876", "A001877", "A001878", "A001899", "A256780" ]
null
N. J. A. Sloane
2024-07-30T01:52:09
oeisdata/seq/A001/A001877.seq
a490fa3a1afa9f9551b73aa856a63fd7
A001878
Number of divisors of n of the form 5k+3; a(0) = 0.
[ "0", "0", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "2", "0", "0", "1", "0", "1", "2", "0", "1", "1", "1", "0", "1", "0", "1", "2", "0", "0", "2", "0", "1", "2", "1", "0", "1", "1", "0", "...
[ "nonn", "easy" ]
25
0
19
[ "A001620", "A001876", "A001877", "A001878", "A001899", "A256848" ]
null
N. J. A. Sloane
2023-11-25T04:35:23
oeisdata/seq/A001/A001878.seq
d0367df5a2b63556a772fb5d5a1795a1
A001879
a(n) = (2n+2)!/(n!*2^(n+1)).
[ "1", "6", "45", "420", "4725", "62370", "945945", "16216200", "310134825", "6547290750", "151242416325", "3794809718700", "102776096548125", "2988412653476250", "92854250304440625", "3070380543400170000", "107655217802968460625", "3989575718580595893750", "15581509612011993962812...
[ "nonn", "easy" ]
98
0
2
[ "A001147", "A001497", "A001814", "A001876", "A001877", "A001878", "A001879", "A002544", "A163938" ]
[ "M4251", "N1775" ]
N. J. A. Sloane
2025-03-15T05:27:57
oeisdata/seq/A001/A001879.seq
98d30a43fd8635445882d82dd95f563d
A001880
Coefficients of Bessel polynomials y_n (x).
[ "1", "15", "210", "3150", "51975", "945945", "18918900", "413513100", "9820936125", "252070693875", "6957151150950", "205552193096250", "6474894082531875", "216659917377028125", "7675951358500425000", "287080580807915895000", "11303797869311688365625", "467445288360359818884375" ]
[ "nonn", "easy" ]
36
4
2
[ "A001147", "A001497", "A001518", "A001880", "A083061", "A094665", "A160470", "A160471", "A160472" ]
[ "M4989", "N2146" ]
N. J. A. Sloane
2018-01-10T19:04:08
oeisdata/seq/A001/A001880.seq
6922c5ad2e2b1c2fec1cb159dbd5009a
A001881
Coefficients of Bessel polynomials y_n (x).
[ "1", "21", "378", "6930", "135135", "2837835", "64324260", "1571349780", "41247931725", "1159525191825", "34785755754750", "1109981842719750", "37554385678684875", "1343291487737574375", "50661278966102805000", "2009564065655411265000", "83648104232906493905625", "36460732492108065...
[ "nonn", "easy" ]
50
5
2
[ "A001497", "A001518", "A001881", "A098503", "A130757" ]
[ "M5116", "N2217" ]
N. J. A. Sloane, Simon Plouffe
2022-09-08T08:44:29
oeisdata/seq/A001/A001881.seq
23d7f2df03af0f17fe63750809f7a4d7
A001882
a(2n) = a(2n-1) + 2a(2n-2), a(2n+1) = a(2n) + a(2n-1), with a(1) = 2 and a(2) = 3.
[ "2", "3", "5", "11", "16", "38", "54", "130", "184", "444", "628", "1516", "2144", "5176", "7320", "17672", "24992", "60336", "85328", "206000", "291328", "703328", "994656", "2401312", "3395968", "8198592", "11594560", "27991744", "39586304", "95569792", ...
[ "nonn" ]
36
1
1
[ "A001882", "A161941" ]
[ "M0730", "N0273" ]
N. J. A. Sloane
2022-04-13T13:25:16
oeisdata/seq/A001/A001882.seq
03f22de4158b5672f2649981c49c0afb
A001883
Number of permutations s of {1,2,...,n} such that |s(i)-i|>1 for each i=1,2,...,n.
[ "1", "0", "0", "0", "1", "4", "29", "206", "1708", "15702", "159737", "1780696", "21599745", "283294740", "3995630216", "60312696452", "970234088153", "16571597074140", "299518677455165", "5711583170669554", "114601867572247060", "2413623459384988298", "532385034927012612...
[ "nonn" ]
104
0
6
[ "A001883", "A001884", "A001891", "A075851", "A075852", "A080018", "A323671" ]
[ "M3630", "N1475" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001883.seq
2969ba9e5e926b8aaedb084c08fbf55f
A001884
Hit polynomials.
[ "1", "0", "1", "2", "20", "104", "775", "6140", "55427", "553802", "6087992", "72994152", "948103477", "13262133736", "198769630061", "3177862894922", "53984653965996", "971068821144112", "18438722595913195", "368558842844143268", "7735520783692157215", "1700950604280411377...
[ "nonn" ]
26
1
4
[ "A001883", "A001884", "A001891", "A080018" ]
[ "M2117", "N0835" ]
N. J. A. Sloane
2021-12-23T22:47:54
oeisdata/seq/A001/A001884.seq
f00ca49c7227b02fa4fe432864ef7f66
A001885
Hit polynomials.
[ "2", "2", "10", "28", "207", "1288", "10366", "91296", "903037", "9832848", "117032570", "1510932116", "21028774738", "313832463386", "4999133311044", "84655108256252", "1518546437350265", "28763765236019284", "573689119174695326", "12017485839703597024", "2637877112089681838...
[ "nonn" ]
20
2
1
[ "A001883", "A001885", "A001891", "A080018" ]
[ "M0384", "N0144" ]
N. J. A. Sloane
2021-12-23T22:45:49
oeisdata/seq/A001/A001885.seq
fec9750de0e2e27a7e5d5782e5f529fd
A001886
Hit polynomials.
[ "3", "6", "44", "180", "1407", "10384", "92896", "911512", "9913152", "117788056", "1519021046", "21123287848", "315034832581", "5015656588706", "84899016219708", "1522394744470356", "28828385427350245", "574839634258405032", "12039133083940334978", "264216869431056251276", "...
[ "nonn" ]
24
3
1
[ "A001883", "A001886", "A001891", "A080018" ]
[ "M2604", "N1031" ]
N. J. A. Sloane
2021-12-23T22:44:05
oeisdata/seq/A001/A001886.seq
0343b0e19fa46dc74fe2cbca11071acf
A001887
Number of permutations p of {1,2,...,n} such that p(i) - i < 0 or p(i) - i > 2 for all i.
[ "1", "0", "0", "0", "1", "5", "33", "236", "1918", "17440", "175649", "1942171", "23396353", "305055960", "4280721564", "64330087888", "1030831875953", "17545848553729", "316150872317105", "6012076099604308", "120330082937778554" ]
[ "nonn" ]
56
0
6
[ "A000255", "A000271", "A001883", "A001887", "A001891", "A075851", "A075852", "A080061" ]
[ "M3970", "N1640" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001887.seq
a506c793ad1e5b9caf5c63f1be022e8a
A001888
Hit polynomials.
[ "1", "1", "1", "4", "21", "122", "849", "6719", "59873", "593686", "6483027", "77309508", "999569969", "13927664613", "208044077633", "3316415176712", "56193522437465", "1008499234742158", "19110533105114433", "381290148293261075", "7989548583615385153", "175418232627066361...
[ "nonn" ]
24
1
4
[ "A001883", "A001888", "A001891", "A080061" ]
[ "M3573", "N1449" ]
N. J. A. Sloane
2021-12-23T22:44:26
oeisdata/seq/A001/A001888.seq
168f0b1dcbe71832124aa8ecf2795242
A001889
Hit polynomials.
[ "1", "4", "8", "38", "209", "1400", "10849", "95516", "938441", "10179149", "120748974", "1554688240", "21588485677", "321561688748", "5113709884902", "86469576394028", "1549114961438599", "29309613834899864", "583986501706555597", "12222118836543561940", "2680602392519787798...
[ "nonn" ]
24
2
2
[ "A001883", "A001889", "A001891", "A080061" ]
[ "M3345", "N1346" ]
N. J. A. Sloane
2021-12-23T22:44:30
oeisdata/seq/A001/A001889.seq
6a8d3b243edccb98e3e09acabe8e4325
A001890
Hit polynomials.
[ "1", "10", "34", "206", "1351", "10543", "92708", "912884", "9917445", "117838808", "1519483258", "21128310078", "315093762147", "5016410089130", "84909414423784", "1522548805068310", "28830824064870329", "574880701875755325", "12039866150973004846", "264230694283295736788", ...
[ "nonn" ]
30
3
2
[ "A001883", "A001890", "A001891", "A080061" ]
[ "M4696", "N2005" ]
N. J. A. Sloane
2018-01-12T23:50:55
oeisdata/seq/A001/A001890.seq
4e059ecff5f8df2eeb56bde0d2020cca
A001891
Hit polynomials; convolution of natural numbers with Fibonacci numbers F(2), F(3), F(4), ....
[ "0", "1", "4", "10", "21", "40", "72", "125", "212", "354", "585", "960", "1568", "2553", "4148", "6730", "10909", "17672", "28616", "46325", "74980", "121346", "196369", "317760", "514176", "831985", "1346212", "2178250", "3524517", "5702824", "9227400", ...
[ "nonn", "easy" ]
97
0
3
[ "A000295", "A001883", "A001890", "A001891", "A001911", "A011794", "A080061", "A152203", "A356619", "A356620", "A356621" ]
[ "M3384", "N1365" ]
N. J. A. Sloane, Simon Plouffe
2025-09-22T16:00:16
oeisdata/seq/A001/A001891.seq
0b0962df54d6044c2e3212d7fd4a99d2
A001892
Number of permutations of (1,...,n) having n-2 inversions (n>=2).
[ "1", "2", "5", "15", "49", "169", "602", "2191", "8095", "30239", "113906", "431886", "1646177", "6301715", "24210652", "93299841", "360490592", "1396030396", "5417028610", "21056764914", "81978913225", "319610939055", "1247641114021", "4875896455975", "19075294462185...
[ "nonn" ]
40
2
2
[ "A001892", "A008302", "A048651" ]
[ "M1477", "N0583" ]
N. J. A. Sloane, R. K. Guy
2025-11-05T15:35:23
oeisdata/seq/A001/A001892.seq
dfc7d918420a1b47f1d7255569db4bc9
A001893
Number of permutations of (1,...,n) having n-3 inversions (n>=3).
[ "1", "3", "9", "29", "98", "343", "1230", "4489", "16599", "61997", "233389", "884170", "3366951", "12876702", "49424984", "190297064", "734644291", "2842707951", "11022366544", "42815701060", "166583279325", "649063995030", "2532267577126", "9891097066760", "38676401...
[ "nonn" ]
37
3
2
[ "A001893", "A008302", "A048651" ]
[ "M2810", "N1132" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001893.seq
a9d504ffa167c99514ba503ee5b78fc6
A001894
Number of permutations of {1,...,n} having n-4 inversions (n>=4).
[ "1", "4", "14", "49", "174", "628", "2298", "8504", "31758", "119483", "452284", "1720774", "6574987", "25214332", "96997223", "374153699", "1446677555", "5605337934", "21758936146", "84604366100", "329453055975", "1284626463105", "5015200610785", "19601107218591", "7...
[ "nonn" ]
33
4
2
[ "A001894", "A008302", "A048651" ]
[ "M3484", "N1416" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001894.seq
a74da27a039001315fc14b00049dcc68
A001895
Number of rooted planar 2-trees with n nodes.
[ "1", "2", "4", "12", "34", "111", "360", "1226", "4206", "14728", "52024", "185824", "668676", "2424033", "8839632", "32412270", "119410390", "441819444", "1641032536", "6116579352", "22870649308", "85764947502", "322476066224", "1215486756372", "4591838372044" ]
[ "nonn", "nice", "easy" ]
32
1
2
[ "A000108", "A000207", "A001895" ]
[ "M1258", "N0481" ]
N. J. A. Sloane
2025-07-08T16:27:08
oeisdata/seq/A001/A001895.seq
b6b7aa4fddb430ff122b3cc2bcf6fe74
A001896
Numerators of cosecant numbers -2*(2^(2*n - 1) - 1)*Bernoulli(2*n); also of Bernoulli(2*n, 1/2) and Bernoulli(2*n, 1/4).
[ "1", "-1", "7", "-31", "127", "-2555", "1414477", "-57337", "118518239", "-5749691557", "91546277357", "-1792042792463", "1982765468311237", "-286994504449393", "3187598676787461083", "-4625594554880206790555", "16555640865486520478399", "-22142170099387402072897" ]
[ "sign", "frac" ]
102
0
3
[ "A001896", "A001897", "A033469", "A036280", "A062715", "A132092", "A132099", "A145901" ]
[ "M4403", "N1858" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001896.seq
7baa14f0c56a87da5732da8563c572d0
A001897
Denominators of cosecant numbers: -2*(2^(2*n-1)-1)*Bernoulli(2*n).
[ "1", "3", "15", "21", "15", "33", "1365", "3", "255", "399", "165", "69", "1365", "3", "435", "7161", "255", "3", "959595", "3", "6765", "903", "345", "141", "23205", "33", "795", "399", "435", "177", "28393365", "3", "255", "32361", "15", "2343"...
[ "nonn", "frac" ]
110
0
2
[ "A001896", "A001897", "A027642", "A033469", "A132092", "A132099", "A160014", "A241171", "A277087", "A340556" ]
[ "M2983", "N1205" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001897.seq
cac0525736b80639a814d1a2277760a3
A001898
Denominators of Bernoulli polynomials B(n)(x).
[ "1", "2", "12", "8", "240", "96", "4032", "1152", "34560", "7680", "101376", "18432", "50319360", "7741440", "6635520", "884736", "451215360", "53084160", "42361159680", "4459069440", "1471492915200", "140142182400", "1758147379200", "152882380800", "417368899584000",...
[ "nonn" ]
25
0
2
[ "A001898", "A027641", "A027642", "A100615", "A100616", "A100655" ]
[ "M2014", "N0749" ]
N. J. A. Sloane
2022-07-25T04:04:49
oeisdata/seq/A001/A001898.seq
15753c037704a97a03388b1b99272b67
A001899
Number of divisors of n of the form 5k+4; a(0) = 0.
[ "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "0", "0", "2", "0", "0", "1", "2", "1", "0", "0", "1", "0", "1", "0", "2", "0", "1", "1", "1", "0", "1", "0", "2", "...
[ "nonn", "easy" ]
28
0
25
[ "A001620", "A001876", "A001877", "A001878", "A001899", "A256849" ]
null
N. J. A. Sloane
2023-11-25T04:34:57
oeisdata/seq/A001/A001899.seq
4f438458d2ffa667ccdcdd650e99aab7
A001900
Successive numerators of Wallis's approximation to Pi/2 (unreduced).
[ "1", "2", "4", "16", "64", "384", "2304", "18432", "147456", "1474560", "14745600", "176947200", "2123366400", "29727129600", "416179814400", "6658877030400", "106542032486400", "1917756584755200", "34519618525593600", "690392370511872000", "13807847410237440000", "30377264...
[ "nonn", "frac", "easy" ]
73
0
2
[ "A000246", "A001900", "A001901", "A001902", "A284230" ]
null
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001900.seq
e28bde7f0f52f48fb3a9e614419fb3b5