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A263146 Expansion of Product_{k>=1} (1+x^(5*k-2))^k.

%I A263146 #8 Oct 12 2015 10:32:41
%S A263146 1,0,0,1,0,0,0,0,2,0,0,2,0,3,0,0,4,0,4,1,0,10,0,5,6,0,16,0,6,14,0,28,
%T A263146 3,7,32,0,40,10,8,63,0,60,33,9,112,3,80,74,10,187,14,110,161,11,300,
%U A263146 46,140,308,13,455,120,182,568,25,672,283,224,968,55,963
%N A263146 Expansion of Product_{k>=1} (1+x^(5*k-2))^k.
%H A263146 Vaclav Kotesovec, <a href="/A263146/b263146.txt">Table of n, a(n) for n = 0..10000</a>
%H A263146 Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015
%F A263146 G.f.: exp(Sum_{j>=1} (-1)^(j+1)/j*x^(3*j)/(1 - x^(5*j))^2).
%F A263146 a(n) ~ 2^(33/100) * 3^(2/3) * 5^(2/3) * Zeta(3)^(1/6) * exp(-Pi^4/(8100*Zeta(3)) + Pi^2 * 3^(2/3) * 2^(1/3) * 5^(2/3) * n^(1/3) / (450*Zeta(3)^(1/3)) + Zeta(3)^(1/3) * 3^(4/3) * 2^(2/3) * 5^(1/3) * n^(2/3) / 20) / (30 * sqrt(Pi) * n^(2/3)).
%t A263146 nmax = 100; CoefficientList[Series[Product[(1+x^(5k-2))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%t A263146 nmax = 100; CoefficientList[Series[E^Sum[(-1)^(j+1)/j*x^(3*j)/(1 - x^(5*j))^2, {j, 1, nmax}], {x, 0, nmax}], x]
%Y A263146 Cf. A263145, A263147, A263148, A263142, A262879.
%K A263146 nonn
%O A263146 0,9
%A A263146 _Vaclav Kotesovec_, Oct 10 2015