%I #9 Apr 19 2017 10:33:12
%S 1,1,2,5,9,17,30,54,94,161,269,449,740,1200,1930,3083,4877,7650,11919,
%T 18444,28363,43341,65848,99523,149654,223901,333448,494427,729996,
%U 1073408,1572264,2294389,3336191,4834261,6981727,10050944,14424665,20639641,29447118
%N Expansion of Product_{k>=1} ((1 + x^k) / (1 - x^(4*k)))^k.
%H Vaclav Kotesovec, <a href="/A285458/b285458.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(1/12 + 3 * (13*Zeta(3))^(1/3) * n^(2/3) / 4) * (13*Zeta(3))^(7/36) / (2 * A * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.
%t nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^(4*k)))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A015128, A000041, A285445, A006950.
%Y Cf. A156616, A000219, A285446, A285459.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Apr 19 2017
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