A381024 Expansion of e.g.f. log(1-x)^2 * exp(x) / (2 * (1-x)).

0, 0, 1, 9, 65, 470, 3634, 30681, 284066, 2878284, 31777851, 380396665, 4912874691, 68142259874, 1010736134108, 15970709345353, 267890182932228, 4755088551397016, 89059375695649173, 1755426336571939497, 36327033843657558661, 787539492771039394158, 17850021806783323801766

Offset: 0

Author

Seiichi Manyama, Feb 12 2025

Keywords

• nonn

Crossrefs

Column k=3 of A269951 (with a different offset).

Cf. A381022.

Programs

Mathematica

nmax=22;CoefficientList[Series[Log[1-x]^2* Exp[x]/ (2* (1-x)),{x,0,nmax}],x]Range[0,nmax]! (* Stefano Spezia, Feb 12 2025 *)

PARI

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

Formula

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

a(n) = A381022(n+1) - A381022(n).