OFFSET
0,4
FORMULA
G.f.: Product_{k>=1} ((1 + x^(2*k-1))/(1 - x^(2*k)))^k.
G.f.: exp(Sum_{k>=1} x^k*((-1)^(k+1) + x^k)/(k*(1 - x^(2*k))^2)).
a(n) ~ exp(3 * (7*Zeta(3))^(1/3) * n^(2/3) / 4 + Pi^2 * n^(1/3) / (24 * (7*Zeta(3))^(1/3)) - Pi^4 / (12096 * Zeta(3)) + 1/12) * (7*Zeta(3))^(7/36) / (A * 2^(23/24) * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Nov 28 2017
MATHEMATICA
nmax = 45; CoefficientList[Series[Product[((1 + x^(2 k - 1))/(1 - x^(2 k)))^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 45; CoefficientList[Series[Exp[Sum[x^k ((-1)^(k + 1) + x^k)/(k (1 - x^(2 k))^2), {k, 1, nmax}]], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 28 2017
STATUS
approved