A346454 a(n) = [x^n] Product_{k>=1} (1 + n^(k+1)*x^k) / (1 - n^(k+1)*x^k).

1, 2, 48, 2592, 223232, 31125000, 6446926080, 1892514990688, 749710432272384, 385769883231774522, 249932498200000000000, 198950665850610546765024, 190770235699567102280073216, 216806274426828873068796386600, 288094786833316639387122903613440

Offset: 0

Author

Vaclav Kotesovec, Jul 19 2021

Keywords

• nonn

Crossrefs

Cf. A344094, A344095, A346452.

Programs

Mathematica

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

Formula

a(n) ~ 2 * n^(2*n).