A381068 Expansion of e.g.f. -log(1-x)^3 * exp(-x) / (6 * (1-x)).

0, 0, 0, 1, 6, 45, 355, 3094, 29596, 309602, 3523110, 43384451, 575296458, 8177866047, 124108103665, 2003376811864, 34282425365912, 620022977756068, 11818804007307308, 236852477229232869, 4978799197426813454, 109547060229435717041, 2518068124265761834239

Offset: 0

Author

Seiichi Manyama, Feb 12 2025

Keywords

• nonn

Crossrefs

Column k=4 of A269954 (with a different offset).

Cf. A381025, A381066.

Programs

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*abs(stirling(k+1, 4, 1)));

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * |Stirling1(k+1,4)|.

a(n) = A381066(n) + A381066(n+1).