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%I #5 Jun 11 2015 06:24:43
%S 1,10,294,10592,433350,19269768,910578172,45070219993,2313935076132,
%T 122371149279812,6631958513821919,366896706349540194,
%U 20656935779581469141,1180759136663178459661,68388869189063880001236,4007252716834400744174729,237231272998203169561835387
%N a(n) = [x^n] Product_{k=1..n} 1/(x^(2*k)*(1-x^k)^3).
%F a(n) ~ c * d^n / n^3, where d = 70.2047644028747363037741119300640924984352825702388550206966992563459... = r^5/(r-1)^3, where r is the root of the equation polylog(2, 1-r) + (5*log(r)^2)/6 = 0, c = 4.0416205700754156... .
%t Table[SeriesCoefficient[1/Product[x^(2*k)*(1-x^k)^3, {k, 1, n}], {x, 0, n}], {n, 0, 20}]
%t Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}]^3, {x, 0, n*(n+2)}], {n, 0, 20}]
%Y Cf. A258788, A258789, A258790, A258791, A258792, A258793, A258795, A258796.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jun 10 2015
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