A381023 Expansion of e.g.f. log(1-x)^4 * exp(x) / 24.

0, 0, 0, 0, 1, 15, 160, 1575, 15659, 163191, 1809905, 21474255, 272757166, 3703523824, 53631736795, 826097224680, 13497286183354, 233291225507890, 4254733292942982, 81680724157089634, 1646873959921840191, 34800264421134754997, 769198023696181428250, 17751664780107823096301

Offset: 0

Author

Seiichi Manyama, Feb 12 2025

Keywords

• nonn

Crossrefs

Column k=4 of A094816.

Cf. A381025.

Programs

Mathematica

nmax=23; CoefficientList[Series[Log[1-x]^4*Exp[x]/24, {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, 4, 1)));

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * |Stirling1(k,4)|.