%I #7 Nov 07 2017 04:22:55
%S 1,2,10,33,110,332,997,2829,7889,21299,56400,146028,371681,929498,
%T 2290296,5562369,13336036,31583177,73957845,171342592,393018517,
%U 893000610,2011039286,4490680381,9947577333,21867539862,47721817473,103420870299,222641160569
%N Expansion of Product_{k>=1} 1/(1 - x^k)^(k*(3*k+1)/2).
%H Vaclav Kotesovec, <a href="/A294667/b294667.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) ~ exp(Pi * 2^(7/4) * n^(3/4) / (3*5^(1/4)) + Zeta(3) * sqrt(5*n) / (sqrt(2) * Pi^2) - 5^(5/4) * Zeta(3)^2 * n^(1/4) / (2^(7/4) * Pi^5) + (25 * Zeta(3)^3) / (6*Pi^8) - 3*Zeta(3) / (8*Pi^2) + 1/24) * Pi^(1/24) / (sqrt(A) * 2^(157/96) * 5^(13/96) * n^(61/96)), where A is the Glaisher-Kinkelin constant A074962.
%t nmax = 30; CoefficientList[Series[Product[1/(1-x^k)^(k*(3*k+1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A294591, A278768.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 06 2017