A381022 Expansion of e.g.f. -log(1-x)^3 * exp(x) / 6.

0, 0, 0, 1, 10, 75, 545, 4179, 34860, 318926, 3197210, 34975061, 415371726, 5328246417, 73470506291, 1084206640399, 17054915985752, 284945098917980, 5040033650314996, 94099409345964169, 1849525745917903666, 38176559589575462327, 825716052360614856485, 18675737859143938658251

Offset: 0

Author

Seiichi Manyama, Feb 12 2025

Keywords

• nonn

Crossrefs

Column k=3 of A094816.

Cf. A381024.

Programs

Mathematica

nmax=23; CoefficientList[Series[-Log[1-x]^3*Exp[x]/6, {x, 0, nmax}], x]Range[0, nmax]! (* Stefano Spezia, Feb 12 2025 *)

PARI

a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(k, 3, 1)));

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * |Stirling1(k,3)|.