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%I #5 Jun 11 2015 06:24:51
%S 1,4,55,896,16494,326422,6812064,147937628,3315019979,76184664934,
%T 1787702723767,42688437971038,1034621287862521,25398832816003228,
%U 630502487733706193,15805630063826901440,399669931534045129915,10184690536676439639278,261340023300544414822171
%N a(n) = [x^n] Product_{k=1..n} 1/(x^(2*k)*(1-x^k)^2).
%F a(n) ~ c * d^n / n^(5/2), where d = 29.1694173246928561008040480794933198469510496062455151175744673506960... = r^4/(r-1)^2, where r is the root of the equation polylog(2, 1-r) + log(r)^2 = 0, c = 2.0036140319464... .
%t Table[SeriesCoefficient[1/Product[x^(2*k)*(1-x^k)^2, {k, 1, n}], {x, 0, n}], {n, 0, 20}]
%t Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}]^2, {x, 0, n*(n+2)}], {n, 0, 20}]
%Y Cf. A258788, A258789, A258791, A258794.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jun 10 2015