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%I #5 Jun 11 2015 06:25:00
%S 1,6,69,915,12978,194688,3051617,49526487,826910754,14135805042,
%T 246508115583,4372617452085,78714369892152,1435357362134796,
%U 26472477913596486,493178852479545556,9270953614684288962,175695092091980786166,3354069936616380522256
%N a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^3).
%F a(n) ~ c * d^n / n^3, where d = 22.0610202494679061193859054301626736218023392292898139172609021542610... = r^4/(r-1)^3, where r is the root of the equation polylog(2, 1-r) + (2*log(r)^2)/3 = 0, c = 20.953639522741... .
%t Table[SeriesCoefficient[1/Product[x^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+3)/2}], {n, 0, 20}]
%Y Cf. A258788, A258790, A258794, A258795, A258796.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jun 10 2015
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