A305209 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - n*x^k))).

1, 1, 2, 12, 86, 885, 11234, 172711, 3112262, 64422126, 1506406702, 39279802969, 1130133725736, 35566642690293, 1215444767739120, 44823725114186355, 1774344335649148230, 75042087586212893216, 3377041177800135323864, 161125608740713509132809, 8124438293071792011560256

Offset: 0

Author

Ilya Gutkovskiy, May 27 2018

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A098407, A292805, A305207.

Programs

Mathematica

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

Formula

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