

A258783


Numerators of a rational sequence related to the closed form evaluation of a Gaussian integer zeta sum.


1



1, 1, 2, 1, 2, 2, 4, 223, 854, 4762, 1444, 2324506, 35548, 140343676, 21047728264, 88824427, 160465442, 96633020222386, 18457536052, 1397584483920886, 885721299987868, 2758893844640044, 3793843972393624, 56271391915038457502, 480348904858674456484, 85734822774933179463764, 2140418040120050844508958552
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OFFSET

1,3


LINKS



FORMULA

p(1) = 1/5, p(n) = (3/((4n+1)*(2n3)))*Sum_{k=1..n1} p(k)*p(nk).
The closed form of the Gaussian integer zeta sum in question is zeta_G(4n) = p(n)*L^(4n)/(4n1), where L is the lemniscate constant.


EXAMPLE

Sequence of fractions begins:
1/5, 1/75, 2/4875, 1/82875, 2/6215625, 2/242409375, 4/19527421875, 223/ 44815433203125, ...


MATHEMATICA

p[1] = 1/5; p[n_] := p[n] = (3/((4n+1)*(2n3)))*Sum[p[k]*p[nk], {k, 1, n1}]; Table[p[n] // Numerator, {n, 1, 30}]


CROSSREFS



KEYWORD

nonn,frac,easy


AUTHOR



STATUS

approved



