A381021 Expansion of e.g.f. log(1-x)^2 * exp(x) / 2.

0, 0, 1, 6, 29, 145, 814, 5243, 38618, 321690, 2995011, 30840304, 348114711, 4274888891, 56744495872, 809667333733, 12358833406580, 200955441549140, 3467781770502885, 63298198354605210, 1218507112218768721, 24671782054230662277, 524152965820457130290

Offset

0,4

Links

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

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * |Stirling1(k,2)|.

Mathematica

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

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(k, 2, 1)));

Crossrefs

Column k=2 of A094816.

Cf. A073596.

Sequence in context: A125785 A186651 A292034 * A108982 A059724 A379198

Adjacent sequences: A381018 A381019 A381020 * A381022 A381023 A381024

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2025

Status

approved