A368754 a(n) = (n!)^n * [x^n] * 1/(1 - polylog(n,x)).

1, 1, 5, 278, 404768, 28436662624, 151309093659896512, 86745908552613198656020224, 7184659625769578063908866060107907072, 110866279942987479997999976181870531647691458347008, 399488258540989429698770032526869852804662313023226648081962369024

Offset: 0

Author

Alois P. Heinz, Jan 04 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A000051, A000142, A007840, A011782, A036740, A323339, A323340, A336258, A336259, A336260, A336261.

Programs

Maple

a:= n-> n!^n*coeff(series(1/(1-polylog(n, x)), x, n+1), x, n):
seq(a(n), n=0..10);
# second Maple program:
b:= proc(n, k) option remember; `if`(n=0, 1,
      add(b(n-j, k)/j^k, j=1..n))
    end:
a:= n-> n!^n*b(n$2):
seq(a(n), n=0..10);

Formula

a(n) = (n!)^n*b(n,n) with b(n,k) = Sum_{j=1..n} b(n-j,k)/j^k for n>0, b(0,k) = 1.