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848d4b7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | from mpmath import mp
mp.dps = 110
def apery_hyper(n):
# A005259(n) = 4F3(-n, -n, n+1, n+1; 1, 1, 1; 1)
return mp.hyper([ -n, -n, n + 1, n + 1 ], [1, 1, 1], 1)
def apery_recurrence(n):
# (m+1)^3 a_{m+1} = (34 m^3 + 51 m^2 + 27 m + 5) a_m - m^3 a_{m-1}
if n == 0:
return 1
if n == 1:
return 5
a_prev = 1
a_cur = 5
for m in range(1, n):
num = (34*m**3 + 51*m**2 + 27*m + 5) * a_cur - (m**3) * a_prev
den = (m + 1) ** 3
a_next = num // den
a_prev, a_cur = a_cur, a_next
return a_cur
def compute():
n = 10
a_exact = apery_recurrence(n) # exact integer
a_hyp = apery_hyper(n) # high-precision hypergeometric evaluation
# sanity check: hypergeometric value should match the exact integer
if abs(a_hyp - mp.mpf(a_exact)) > mp.mpf('1e-90'):
raise ValueError("Consistency check failed")
return a_exact
if __name__ == "__main__":
print(str(compute())) |