cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A304460 Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(n^3).

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%I A304460 #6 May 13 2018 05:16:54
%S A304460 1,1,44,4410,905840,318906400,172185088824,132357574570221,
%T A304460 137406570363495360,185242628827767255255,314645673306845990409300,
%U A304460 657405676947400829561901359,1656968286301847988118098735168,4957425610652588047512198547937050
%N A304460 Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(n^3).
%C A304460 In general, for m>=3, coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(n^m) is asymptotic to n^(m*n)/n!.
%F A304460 a(n) ~ exp(n) * n^(2*n - 1/2) / sqrt(2*Pi).
%t A304460 nmax = 20; Table[SeriesCoefficient[Product[1/(1-x^k)^(n^3), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
%t A304460 nmax = 20; Table[SeriesCoefficient[1/QPochhammer[x]^(n^3), {x, 0, n}], {n, 0, nmax}]
%Y A304460 Cf. A008485, A023872, A304446, A304459.
%K A304460 nonn
%O A304460 0,3
%A A304460 _Vaclav Kotesovec_, May 13 2018