A381106 Expansion of e.g.f. -log(1-x)^3 * (exp(x) - 1) / 6.

0, 0, 0, 0, 4, 40, 320, 2555, 21728, 200802, 2024510, 22221485, 264453750, 3396686865, 46873789235, 692049842575, 10889098371032, 181952854080860, 3218431205690356, 60087159752141449, 1180916015576750386, 24372799835934758327, 527084149497398472485, 11919591185373007970251

Offset: 0

Author

Seiichi Manyama, Feb 14 2025

Keywords

• nonn

Crossrefs

Cf. A052863, A381105.

Cf. A000399, A381022.

Programs

PARI

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

Formula

a(n) = Sum_{k=0..n-1} binomial(n,k) * |Stirling1(k,3)|.

a(n) = A381022(n) - A000399(n).