A305255 a(n) = [x^n] exp(Sum_{k>=1} (-1)^k*x^k/(k*(1 - x^k)^n)).

1, -1, -1, -4, -3, 14, 240, 1686, 9479, 36761, 3412, -1951731, -27296124, -268495319, -2093667873, -11586874946, -3788945531, 1127535019748, 21900095232973, 297591401221473, 3270627818325128, 28116733997044842, 129815302615081267, -1568168714539146596, -59839621829784309343

Offset: 0

Author

Ilya Gutkovskiy, May 28 2018

Keywords

• sign

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A255528, A293554, A294846, A305205, A305206.

Programs

Mathematica

Table[SeriesCoefficient[Exp[Sum[(-1)^k x^k/(k (1 - x^k)^n), {k, 1, n}]], {x, 0, n}], {n, 0, 24}]
Table[SeriesCoefficient[Product[1/(1 + x^k)^Binomial[n + k - 2, n - 1], {k, 1, n}], {x, 0, n}], {n, 0, 24}]

Formula

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