A246241 Sum of sixth powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n.

1, 1, 66, 51033, 227263876, 3942914312505, 207874071367118436, 28034487027123336138967, 8522964991458712709499563784, 5302659152501095787067079018931409, 6255441983177258421672575234559926069140, 13154762734940720943667470423246456789300752691

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=6 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)^5/j!, j=0..n)))
    end:
a:= n-> n!*b(n$2):
seq(a(n), n=0..15);

Formula

a(n) = [x^n] (n!)^6 * (Sum_{j=0..n} x^j/(j!)^6)^n.