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%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
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