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%I #6 May 28 2015 03:37:59
%S 1,0,2,6,13,32,69,160,344,760,1601,3384,7022,14434,29361,59140,118089,
%T 233754,459293,895382,1733904,3334914,6374654,12111632,22881777,
%U 42993244,80362496,149464404,276657082,509740278,935046158,1707916988,3106810873,5629121054
%N Expansion of Product_{k>=1} (1+x^k)^(k*(k-1)).
%H Vaclav Kotesovec, <a href="/A258344/b258344.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ 7^(1/8) / (2^(43/24) * 15^(1/8) * n^(5/8)) * exp(-2025*Zeta(3)^3 / (49*Pi^8) - 135*(15/14)^(1/4) * Zeta(3)^2 / (14*Pi^5) * n^(1/4) - 3*sqrt(15/14) * Zeta(3) / Pi^2 * sqrt(n) + 2*(14/15)^(1/4)*Pi/3 * n^(3/4)), where Zeta(3) = A002117.
%t nmax=50; CoefficientList[Series[Product[(1+x^k)^(k*(k-1)),{k,1,nmax}],{x,0,nmax}],x]
%Y Cf. A027998, A028377, A027999, A258341, A258342, A258343, A258345, A258346, A258348.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, May 27 2015
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