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%I #13 Apr 16 2017 07:09:36
%S 1,1,2,5,4,12,20,29,53,80,127,199,311,468,715,1079,1621,2402,3541,
%T 5210,7574,11046,15926,22917,32804,46766,66419,93936,132331,185830,
%U 260144,362752,504573,699376,966842,1332721,1832217,2512209,3435932,4687884,6380911
%N Expansion of Product_{k>=1} (1 + x^k)^k / (1 + x^(4*k))^(4*k).
%H Seiichi Manyama, <a href="/A285292/b285292.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Vaclav Kotesovec)
%F a(n) ~ exp(3^(5/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2^(3/4) * 3^(1/6) * sqrt(Pi) * n^(2/3)).
%t nmax = 50; CoefficientList[Series[Product[(1+x^k)^k/(1+x^(4*k))^(4*k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A262736, A262924, A285293.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Apr 16 2017