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A281683
Expansion of Product_{k>=1} (1 - x^(2*k-1))^(2*k-1)/(1 - x^(2*k))^(2*k).
3
1, -1, 2, -5, 10, -18, 32, -59, 106, -181, 305, -518, 867, -1418, 2301, -3724, 5966, -9448, 14862, -23263, 36165, -55802, 85609, -130732, 198574, -299941, 450946, -675153, 1006395, -1493598, 2207928, -3251926, 4771934, -6977018, 10166502, -14766512, 21379861
OFFSET
0,3
LINKS
FORMULA
a(n) = (-1)^n * A224364(n).
a(n) ~ (-1)^n * exp(1/6 + 3 * 2^(-5/3) * (7*Zeta(3))^(1/3) * n^(2/3)) * (7*Zeta(3))^(2/9) / (2^(25/36) * A^2 * sqrt(3*Pi) * n^(13/18)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Nov 09 2017
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 - x^k)^k/(1 - x^(2*k))^(4*k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 09 2017 *)
nmax = 50; CoefficientList[Series[Product[1/((1 + x^k)^(4*k)*(1 - x^k)^(3*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 09 2017 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 14 2017
STATUS
approved