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

%I A368754 #17 Jan 05 2024 18:44:39
%S A368754 1,1,5,278,404768,28436662624,151309093659896512,
%T A368754 86745908552613198656020224,7184659625769578063908866060107907072,
%U A368754 110866279942987479997999976181870531647691458347008,399488258540989429698770032526869852804662313023226648081962369024
%N A368754 a(n) = (n!)^n * [x^n] * 1/(1 - polylog(n,x)).
%H A368754 Alois P. Heinz, <a href="/A368754/b368754.txt">Table of n, a(n) for n = 0..30</a>
%F A368754 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.
%p A368754 a:= n-> n!^n*coeff(series(1/(1-polylog(n, x)), x, n+1), x, n):
%p A368754 seq(a(n), n=0..10);
%p A368754 # second Maple program:
%p A368754 b:= proc(n, k) option remember; `if`(n=0, 1,
%p A368754       add(b(n-j, k)/j^k, j=1..n))
%p A368754     end:
%p A368754 a:= n-> n!^n*b(n$2):
%p A368754 seq(a(n), n=0..10);
%Y A368754 Cf. A000051, A000142, A007840, A011782, A036740, A323339, A323340, A336258, A336259, A336260, A336261.
%K A368754 nonn
%O A368754 0,3
%A A368754 _Alois P. Heinz_, Jan 04 2024