A304446 - OEIS

%I #7 May 13 2018 03:02:10

%S 1,1,14,255,6460,209405,8287038,387605491,20930373880,1281932464680,

%T 87828985857380,6656774777650459,553068813860022264,

%U 49988877225605011590,4883606791114233989450,512829418039842285746460,57607740718731604241384432,6893420862444517638234527039

%N Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(n^2).

%H Vaclav Kotesovec, <a href="/A304446/b304446.txt">Table of n, a(n) for n = 0..330</a>

%F a(n) ~ exp(n + 3/2) * n^(n - 1/2) / sqrt(2*Pi).

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

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

%Y Cf. A008485, A023871, A304445.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, May 12 2018