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

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

Offset

0,3

Links

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

Formula

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

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

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 *)

Prog

(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)))

Crossrefs

Cf. A006252, A320083, A351133, A351134.

Cf. A350721, A351117, A351138.

Sequence in context: A218142 A117579 A249584 * A107122 A059113 A057839

Adjacent sequences: A351132 A351133 A351134 * A351136 A351137 A351138

Keyword

nonn

Author

Seiichi Manyama, Feb 02 2022

Status

approved