A345759 E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k / k!).

1, -1, -2, -2, 7, 78, 513, 2665, 9406, -13902, -789143, -11806456, -140040408, -1463842226, -13377115923, -95264642343, -198034245627, 11021440199748, 322964047973519, 6617250866231379, 118668721540190350, 1965786734149801960, 30348547043773563767

Offset: 0

Author

Seiichi Manyama, Jun 26 2021

Keywords

• sign

Comments

Stirling transform of A185895.

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Stirling Transform

Crossrefs

Cf. A048993, A140585, A185895, A305547.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, 1-(exp(x)-1)^k/k!)))

Formula

a(n) = Sum_{k=0..n} Stirling2(n,k) * A185895(k).