A351281 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..15.

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

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 *)

PROG

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