A305207 a(n) = [x^n] exp(Sum_{k>=1} x^k/(k*(1 - n*x^k))).

1, 1, 3, 13, 95, 921, 11586, 176324, 3162447, 65233120, 1521743103, 39609506223, 1138093049808, 35779807446670, 1221719353617885, 45025117385882889, 1781345658408660655, 75304205654268663567, 3387556543611248410593, 161575661076504392490150, 8144909167115962980271095

Offset: 0

Author

Ilya Gutkovskiy, May 27 2018

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A034691, A104460, A252654, A305209.

Programs

Mathematica

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

Formula

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