A304446 Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(n^2).

1, 1, 14, 255, 6460, 209405, 8287038, 387605491, 20930373880, 1281932464680, 87828985857380, 6656774777650459, 553068813860022264, 49988877225605011590, 4883606791114233989450, 512829418039842285746460, 57607740718731604241384432, 6893420862444517638234527039

Offset: 0

Author

Vaclav Kotesovec, May 12 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..330

Crossrefs

Cf. A008485, A023871, A304445.

Programs

Mathematica

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

Formula

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