A381065 Expansion of e.g.f. -log(1-x)^3 * exp(-x) / 6.

0, 0, 0, 1, 2, 15, 85, 609, 4844, 43238, 427090, 4630241, 54683046, 699012093, 9617979007, 141755256889, 2228396376088, 37221746535564, 658390407698084, 12295201090394017, 241749652842156074, 4992277083472634507, 108032799218176059337, 2444797394606939402449

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

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

Prog

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

Crossrefs

Column k=3 of A269953.

Cf. A381022, A381067.

Sequence in context: A383947 A328007 A098624 * A116079 A153445 A376135

Adjacent sequences: A381062 A381063 A381064 * A381066 A381067 A381068

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2025

Status

approved