A381108 Expansion of e.g.f. log(1-x)^2 * (exp(x) - 1) / (2 * (1-x)).

0, 0, 0, 3, 30, 245, 2010, 17549, 165942, 1705584, 19024275, 229478689, 2981315139, 41545542818, 618579336284, 9804891730633, 164897938095108, 2933486106772376, 55047126101826453, 1086816606230786217, 22523274090016854661, 488907589907823010158, 11093875133012393113766

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) = A381024(n) - A000399(n+1).

Prog

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

Crossrefs

Cf. A002627, A381107.

Cf. A000399, A381024.

Sequence in context: A130546 A051133 A332426 * A043030 A178015 A120689

Adjacent sequences: A381105 A381106 A381107 * A381109 A381110 A381111

Keyword

nonn

Author

Seiichi Manyama, Feb 14 2025

Status

approved