A319754 a(n) = [x^n] Product_{k>=1} (1 - x^k)/(1 - n*x^k).

1, 0, 3, 24, 252, 3096, 46620, 823152, 16776648, 387413208, 9999989010, 285311493720, 8916100178843, 302875101365928, 11112006817455180, 437893890197853824, 18446744073423298800, 827240261878925204256, 39346408075284871499214, 1978419655659972977219880

Offset: 0

Author

Ilya Gutkovskiy, Sep 27 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386

Crossrefs

Main diagonal of A319753.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1 - x^k)/(1 - n x^k), {k, 1, n}], {x, 0, n}], {n, 0, 19}]
Table[SeriesCoefficient[Exp[Sum[Sum[d (n^(k/d) - 1), {d, Divisors[k]}] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 19}]

Formula

a(n) = [x^n] exp(Sum_{k>=1} ( Sum_{d|k} d*(n^(k/d) - 1) ) * x^k/k).

a(n) ~ n^n. - Vaclav Kotesovec, Sep 27 2018