A343928 a(n) = Sum_{k=0..n} (k!)^n * binomial(n,k).

1, 2, 7, 244, 337061, 24923091206, 139331988275478727, 82607113404338664216300296, 6984967577834038055008791270166057993, 109110690950275218023122492287310115968068596613130, 395940866518366059877297056617763923418318903997411043997258716171

Offset: 0

Author

Seiichi Manyama, May 04 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..30

Crossrefs

Cf. A000522, A046662, A072034, A336247, A339311, A343898, A343899, A343929.

Programs

Mathematica

a[n_] := Sum[(k!)^n * Binomial[n, k], {k, 0, n} ]; Array[a, 11, 0] (* Amiram Eldar, May 04 2021 *)

PARI

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

Formula

a(n) = [x^n] Sum_{k>=0} (k!)^n * x^k/(1 - x)^(k+1).

a(n) = n! * [x^n] exp(x) * Sum_{k>=0} (k!)^(n-1) * x^k.