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

0,4

Links

Table of n, a(n) for n=0..24.

N. J. A. Sloane, Transforms

Formula

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

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}]

Crossrefs

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

Sequence in context: A197883 A222195 A292413 * A358281 A095332 A195586

Adjacent sequences: A305252 A305253 A305254 * A305256 A305257 A305258

Keyword

sign

Author

Ilya Gutkovskiy, May 28 2018

Status

approved