A305206 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k)^n)).

1, 1, 2, 9, 36, 190, 1070, 6797, 46942, 350901, 2806187, 23894662, 215598410, 2053090936, 20557071012, 215697357449, 2364810631734, 27023086395647, 321160376470277, 3962047673946906, 50648323260067319, 669819485900273336, 9150740338219903590, 128965789655207156299

Offset: 0

Author

Ilya Gutkovskiy, May 27 2018

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A026007, A028377, A258343, A293554, A305205.

Programs

Mathematica

Table[SeriesCoefficient[Exp[Sum[(-1)^(k + 1) x^k/(k (1 - x^k)^n), {k, 1, n}]], {x, 0, n}], {n, 0, 23}]
Table[SeriesCoefficient[Product[(1 + x^k)^Binomial[n + k - 2, n - 1], {k, 1, n}], {x, 0, n}], {n, 0, 23}]

Formula

a(n) = [x^n] Product_{k>=1} (1 + x^k)^binomial(n+k-2,n-1).