A351281 a(n) = Sum_{k=0..n} k! * k^k * Stirling2(n,k).

1, 1, 9, 187, 7173, 440611, 39631509, 4910795107, 802015652853, 166948755155971, 43146953460348309, 13555255072473665827, 5087595330217093070133, 2248298922174973220446531, 1155512971750307157457879509, 683392198848998191062416885347

Offset: 0

Author

Seiichi Manyama, Feb 06 2022

Keywords

• nonn

Crossrefs

Cf. A000670, A122399, A229234, A282190, A350722, A351280.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k! * k^k * StirlingS2[n, k], {k, 1, n}]; Array[a, 16, 0] (* Amiram Eldar, Feb 06 2022 *)

PARI

a(n) = sum(k=0, n, k!*k^k*stirling(n, k, 2));

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*(exp(x)-1))^k)))

Formula

E.g.f.: Sum_{k>=0} (k * (exp(x) - 1))^k.

a(n) ~ exp(exp(-1)/2) * n! * n^n. - Vaclav Kotesovec, Feb 06 2022