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%I #7 Oct 01 2015 01:58:42
%S 1,3,10,25,62,136,293,590,1165,2205,4097,7391,13120,22780,38997,65613,
%T 109036,178660,289575,463842,735870,1155717,1799620,2777795,4254859,
%U 6467115,9761770,14633605,21799465,32273399,47506759,69537814,101252595,146675875,211451893
%N Expansion of Product_{k>=1} 1/((1+x^k)*(1-x^k)^4).
%C In general, if m > 1 and g.f. = Product_{k>=1} 1/((1+x^k)*(1-x^k)^m), then a(n) ~ exp(sqrt((2*m-1)*n/3)*Pi) * (2*m-1)^((m+1)/4) / (2^(m+1) * 3^((m+1)/4) * n^((m+3)/4)).
%H 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, p. 16.
%F a(n) ~ exp(sqrt(7*n/3)*Pi) * 7^(5/4) / (32 * 3^(5/4) * n^(7/4)).
%t nmax = 50; CoefficientList[Series[Product[1/((1 + x^k)*(1 - x^k)^4), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A002513 (m=2), A029863 (m=3), A261998.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Sep 20 2015
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