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Coefficient of x^n in Product_{k>=1} (1+x^k)^(n^3).
2

%I #7 May 13 2018 05:16:59

%S 1,1,36,3681,770576,276218900,151479085752,117975860569973,

%T 123825991870849088,168480096257782525419,288418999876101261408100,

%U 606652152400218992684850772,1537897976017806908644807294656,4624364862288125600795358272563097

%N Coefficient of x^n in Product_{k>=1} (1+x^k)^(n^3).

%C In general, for m>=3, coefficient of x^n in Product_{k>=1} (1+x^k)^(n^m) is asymptotic to n^(m*n)/n!.

%F a(n) ~ exp(n) * n^(2*n - 1/2) / sqrt(2*Pi).

%t nmax = 20; Table[SeriesCoefficient[Product[(1+x^k)^(n^3), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

%t nmax = 20; Table[SeriesCoefficient[(QPochhammer[-1, x]/2)^(n^3), {x, 0, n}], {n, 0, nmax}]

%Y Cf. A248882, A270913, A304445, A304460.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, May 13 2018