A246240 Sum of fifth powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n.

1, 1, 34, 9237, 11007556, 41262262505, 393602334214536, 8250608306349317503, 341379009411431516029576, 25693424488177173143564108049, 3298778490446719483156753593432700, 686045693667123232536420797701863401231, 221475400673152122602874526565943771742514376

Offset: 0

Author

Alois P. Heinz, Aug 19 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Column k=5 of A245397.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(b(n-j, i-1)*binomial(n, j)^4/j!, j=0..n)))
    end:
a:= n-> n!*b(n$2):
seq(a(n), n=0..15);

Formula

a(n) = [x^n] (n!)^5 * (Sum_{j=0..n} x^j/(j!)^5)^n.