A245398 Sum of n-th powers of coefficients in full expansion of (z_1 + z_2 + ... + z_n)^n.

1, 1, 6, 381, 591460, 41262262505, 207874071367118436, 110807909819808911886548575, 8558639841332633529404511878004186120, 124773193097402414339622625011223384066643153613969, 431220070110830123225191271755402469908417673177630594034899052340

Offset: 0

Author

Alois P. Heinz, Jul 21 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..30

Crossrefs

Main diagonal of A245397.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0 or i=1, 1,
      add(b(n-j, i-1, k)*binomial(n, j)^k, j=0..n))
    end:
a:= n-> b(n$3):
seq(a(n), n=0..12);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0,
   Sum[b[n-j, i-1, k]*Binomial[n, j]^(k-1)/j!, {j, 0, n}]]];
a[n_] := n!*b[n, n, n];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Jun 27 2022, after Alois P. Heinz *)

Formula

a(n) = [x^n] (n!)^n * (Sum_{j=0..n} x^j/(j!)^n)^n.

a(n) = A245397(n,n).