A304445 Coefficient of x^n in Product_{k>=1} (1+x^k)^(n^2).

1, 1, 10, 174, 4132, 126905, 4802046, 216313349, 11313533064, 674172155790, 45102830448510, 3347925678474168, 273085613904116184, 24282144087974698445, 2337736453663291696624, 242272777074973285192935, 26892702305505020726198800, 3183326728470139531614913088

Offset: 0

Author

Vaclav Kotesovec, May 12 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A027998, A270913, A304446.

Programs

Mathematica

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

Formula

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