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

0,4

Links

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

Formula

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

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

Prog

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

Crossrefs

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

Cf. A016269, A381024, A381065.

Sequence in context: A001541 A322242 A356392 * A330626 A161940 A074565

Adjacent sequences: A381064 A381065 A381066 * A381068 A381069 A381070

Keyword

nonn,new

Author

Seiichi Manyama, Feb 12 2025

Status

approved