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%I #8 Nov 29 2017 03:41:13
%S 1,1,2,4,6,11,19,30,47,76,118,181,277,417,624,929,1367,2001,2913,4210,
%T 6056,8665,12328,17466,24640,34600,48395,67442,93625,129520,178588,
%U 245429,336252,459324,625613,849762,1151150,1555378,2096332,2818630,3780903,5060240,6757633,9005106,11975265
%N Expansion of Product_{k>=1} ((1 + x^(2*k))/(1 - x^(2*k-1)))^k.
%F G.f.: Product_{k>=1} ((1 + x^(2*k))/(1 - x^(2*k-1)))^k.
%F G.f.: exp(Sum_{k>=1} x^k*(1 - (-1)^k*x^k)/(k*(1 - x^(2*k))^2)).
%F a(n) ~ exp(3*(7*Zeta(3))^(1/3) * n^(2/3) / 4 + Pi^2 * n^(1/3) / (12 * (7*Zeta(3))^(1/3)) - Pi^4 / (3024*Zeta(3)) - 1/24) * A^(1/2) * (7*Zeta(3))^(11/72) / (2^(11/8) * sqrt(3*Pi) * n^(47/72)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Nov 28 2017
%t nmax = 44; CoefficientList[Series[Product[((1 + x^(2 k))/(1 - x^(2 k - 1)))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 44; CoefficientList[Series[Exp[Sum[x^k (1 - (-1)^k x^k)/(k (1 - x^(2 k))^2), {k, 1, nmax}]], {x, 0, nmax}], x]
%Y Cf. A001935, A001936, A001937, A026007, A035528, A093160, A113415, A156616, A284474, A292037, A295832.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Nov 28 2017
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