A351135 a(n) = Sum_{k=0..n} k! * k^(k*n) * Stirling1(n,k).

1, 1, 31, 117716, 103060088854, 35762522985456876854, 7426384178533125493811949517898, 1294894823429942179301223205449027573956692920, 253092741940931724343266089700550691376738432767085871485096840

Offset: 0

Author

Seiichi Manyama, Feb 02 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..26

Crossrefs

Cf. A006252, A320083, A351133, A351134.

Cf. A350721, A351117, A351138.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k! * k^(k*n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 9, 0] (* Amiram Eldar, Feb 02 2022 *)

PARI

a(n) = sum(k=0, n, k!*k^(k*n)*stirling(n, k, 1));

PARI

my(N=10, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k^k*x)^k)))

Formula

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

a(n) ~ n! * n^(n^2). - Vaclav Kotesovec, Feb 03 2022