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%I #8 Apr 16 2017 06:15:13
%S 1,1,2,5,7,15,26,44,74,125,205,331,534,844,1332,2077,3215,4934,7533,
%T 11410,17191,25751,38346,56833,83814,123025,179776,261639,379186,
%U 547476,787516,1128775,1612395,2295701,3258177,4610130,6503873,9149365,12835612,17959085
%N Expansion of Product_{k>=1} ((1 + x^k) / (1 + x^(4*k)))^k.
%H Vaclav Kotesovec, <a href="/A285290/b285290.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(2^(-8/3) * 3^(5/3) * (5*Zeta(3))^(1/3) * n^(2/3)) * (5*Zeta(3))^(1/6) / (2^(4/3) * 3^(1/6) * sqrt(Pi) * n^(2/3)).
%t nmax = 50; CoefficientList[Series[Product[((1+x^k)/(1+x^(4*k)))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A285289, A263345, A285291.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Apr 16 2017