A336295 - OEIS

%I #8 Jul 27 2023 16:57:18

%S 1,1,5,251,359200,25822962624,141766192358448256,

%T 83301485967496541735457536,7013555995366382867427754604471779328,

%U 109330254486209621988088555707809713786027354619904,396335044092985772297627538614627390881554195217999599121962369024

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

%H Alois P. Heinz, <a href="/A336295/b336295.txt">Table of n, a(n) for n = 0..30</a>

%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       b(n, i-1, k)+b(n-i, min(n-i, i), k)*((i-1)!*binomial(n, i))^k))

%p     end:

%p a:= n-> b(n$3):

%p seq(a(n), n=0..12);  # _Alois P. Heinz_, Jul 27 2023

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

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jul 16 2020