A336295 a(n) = (n!)^n * [x^n] Product_{k>=1} 1/(1 - x^k/k^n).

1, 1, 5, 251, 359200, 25822962624, 141766192358448256, 83301485967496541735457536, 7013555995366382867427754604471779328, 109330254486209621988088555707809713786027354619904, 396335044092985772297627538614627390881554195217999599121962369024

Offset: 0

Author

Ilya Gutkovskiy, Jul 16 2020

Keywords

• nonn

Links

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

Crossrefs

Cf. A007841, A215910, A249588, A249593, A269791, A269793, A269794.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k)+b(n-i, min(n-i, i), k)*((i-1)!*binomial(n, i))^k))
    end:
a:= n-> b(n$3):
seq(a(n), n=0..12);  # Alois P. Heinz, Jul 27 2023

Mathematica

Table[(n!)^n SeriesCoefficient[Product[1/(1 - x^k/k^n), {k, 1, n}], {x, 0, n}], {n, 0, 10}]