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%I #14 Apr 17 2017 07:38:32
%S 1,-1,-1,-2,5,-4,0,-6,26,-16,6,-31,93,-81,19,-147,310,-295,136,-486,
%T 1069,-940,645,-1575,3338,-3021,2301,-5089,9735,-9381,7548,-15506,
%U 27556,-27587,23664,-44862,76043,-77620,70982,-124744,204389,-211376,203644,-336775
%N Expansion of Product_{k>=1} (1 + x^(4*k))^(4*k) / (1 + x^k)^k.
%H Seiichi Manyama, <a href="/A285295/b285295.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ (-1)^n * exp(-1/12 + 3 * (5*Zeta(3))^(1/3) * n^(2/3) / 4) * A * (5*Zeta(3))^(5/36) / (2^(5/4) * sqrt(3*Pi) * n^(23/36)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Apr 17 2017
%t nmax = 50; CoefficientList[Series[Product[(1 + x^(4*k))^(4*k) / (1 + x^k)^k, {k,1,nmax}], {x,0,nmax}], x] (* _Vaclav Kotesovec_, Apr 16 2017 *)
%Y Product_{k>=1} (1 + x^(m*k))^(m*k) / (1 + x^k)^k: A284628 (m=2), A285294 (m=3), this sequence (m=4).
%Y Cf. A285292.
%K sign
%O 0,4
%A _Seiichi Manyama_, Apr 16 2017
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