A350721 a(n) = Sum_{k=0..n} k! * k^(k+n) * Stirling1(n,k).

1, 1, 31, 4184, 1495534, 1110325474, 1481505320078, 3225820132807320, 10696978730747904696, 51287741246274865567776, 341442095880058160040860592, 3055472627228313328903357352784, 35788671820468495762774011478900032

Offset: 0

Author

Seiichi Manyama, Feb 03 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..161

Crossrefs

Cf. A320083, A350719, A350720.

Cf. A350722, A351135.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k! * k^(k+n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 13, 0] (* Amiram Eldar, Feb 03 2022 *)

PARI

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

PARI

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

Formula

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

a(n) ~ exp(-exp(-2)/2) * n! * n^(2*n). - Vaclav Kotesovec, Feb 04 2022