A351280 a(n) = Sum_{k=0..n} k! * k^k * Stirling1(n,k).

1, 1, 7, 140, 5254, 318854, 28455182, 3506576856, 570360248856, 118356589567440, 30512901324706608, 9566812017770347152, 3584662956711860108352, 1581905384865801328253712, 812047187127758913474118032, 479763784808095613489811245568

Offset

0,3

Links

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

Formula

E.g.f.: Sum_{k>=0} (k * log(1+x))^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 * StirlingS1[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, 1));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*log(1+x))^k)))

Crossrefs

Cf. A006252, A305819, A320083, A350721, A350725, A351281.

Sequence in context: A297650 A085708 A054606 * A306628 A302912 A191956

Adjacent sequences: A351277 A351278 A351279 * A351281 A351282 A351283

Keyword

nonn

Author

Seiichi Manyama, Feb 06 2022

Status

approved