A304448 Coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(n^2).

1, 2, 40, 1320, 61984, 3797560, 287566368, 25957422400, 2721948311680, 325260627848442, 43635601119149040, 6494550360714973304, 1062063969900788407680, 189301256401392643093560, 36526821128512112807216192, 7585918627122817713267856320

Offset: 0

Author

Vaclav Kotesovec, May 12 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A206622, A270919, A304445, A304446, A304447.

Programs

Mathematica

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

Formula

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