A305205 a(n) = [x^n] exp(-Sum_{k>=1} x^k/(k*(1 - x^k)^n)).

1, -1, -2, -3, -4, 30, 274, 1841, 9358, 32463, -41557, -2265846, -28939286, -272101778, -2038274408, -10494221259, 9056975574, 1244820826687, 22703501504125, 299864024917632, 3221417281127823, 26849622543478562, 110101743392268978, -1810492304600468063

Offset: 0

Author

Ilya Gutkovskiy, May 27 2018

Keywords

• sign

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A073592, A292386, A292387, A293554, A305206.

Programs

Mathematica

Table[SeriesCoefficient[Exp[-Sum[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).