A345752 E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k / k).

1, -1, -2, -3, 0, 55, 572, 4865, 40912, 351675, 2978196, 23418373, 148849544, 84185855, -27459134420, -881482705719, -21652972750464, -487503384038525, -10785437160748156, -242968902040697011, -5627949704687484872, -133358411031825299385

Offset: 0

Author

Seiichi Manyama, Jun 26 2021

Keywords

• sign

Comments

Stirling transform of A292359.

Links

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

Crossrefs

Cf. A048993, A292359, A305986, A305987, A345751.

Programs

Mathematica

max = 21; Range[0, max]! * CoefficientList[Series[Product[1 - (Exp[x] - 1)^k/k, {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Jun 26 2021 *)

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) * A292359(k).