A381067 Expansion of e.g.f. log(1-x)^2 * exp(-x) / (2 * (1-x)).

0, 0, 1, 3, 17, 100, 694, 5453, 48082, 470328, 5057331, 59313287, 753695139, 10316991100, 151373235896, 2370151632977, 39450142911652, 695612154233648, 12953591498092101, 254044853932550091, 5234026736314790581, 113025076301648693844, 2552830193825115461786

Offset: 0

Author

Seiichi Manyama, Feb 12 2025

Keywords

• nonn

Crossrefs

Column k=3 of A269954 (with a different offset).

Cf. A016269, A381024, A381065.

Programs

PARI

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

Formula

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

a(n) = A381065(n) + A381065(n+1).