A382701 Expansion of e.g.f. -log(1 - x)^3 * exp(3*x) / 6.

0, 0, 0, 1, 18, 215, 2205, 21469, 209356, 2111318, 22448130, 254297241, 3083362326, 40046861205, 556384764663, 8248646054349, 130120383122136, 2177629350914412, 38552967519050628, 720104832324072081, 14154891429467595258, 292132391046470467443, 6316572474787017069297

Offset

0,5

Links

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

Formula

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

Prog

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

Crossrefs

Column k=3 of A327997.

Cf. A381022.

Sequence in context: A260569 A125430 A021764 * A059357 A324638 A009470

Adjacent sequences: A382698 A382699 A382700 * A382702 A382703 A382704

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2025

Status

approved