A381105 Expansion of e.g.f. log(1-x)^2 * (exp(x) - 1) / 2.

0, 0, 0, 3, 18, 95, 540, 3479, 25550, 212106, 1968435, 20211664, 227570871, 2788446011, 36941736832, 526201686373, 8019670404980, 130221159155540, 2244376179923685, 40921210296083610, 786941965401130321, 15918834017469062277, 337908155040286890290, 7510104219030171089935

Offset: 0

Author

Seiichi Manyama, Feb 14 2025

Keywords

• nonn

Crossrefs

Cf. A052863, A381106.

Cf. A000254, A381021.

Programs

PARI

a(n) = sum(k=0, n-1, binomial(n, k)*abs(stirling(k, 2, 1)));

Formula

a(n) = Sum_{k=0..n-1} binomial(n,k) * |Stirling1(k,2)|.

a(n) = A381021(n) - A000254(n-1).