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%I #12 Aug 29 2022 16:35:56
%S 1,0,-4,-27,-64,4375,199584,6739607,169934848,-1012395105,
%T -709624000000,-86599643309201,-8221227668471808,-638169258399740977,
%U -27617164284655812608,3853095093357099609375,1568756883209662050074624,360407172063462944082773311
%N a(n) = Sum_{k=0..n} (-1)^k * (k*n+1)^(n-k) * binomial(n,k).
%F a(n) = n! * [x^n] exp( x * (1 - exp(n * x)) ).
%F a(n) = [x^n] Sum_{k>=0} (-x)^k / (1 - (n*k+1)*x)^(k+1).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * n^(n-k) * Stirling2(n-k,k)/(n-k)!.
%o (PARI) a(n) = sum(k=0, n, (-1)^k*(k*n+1)^(n-k)*binomial(n, k));
%o (PARI) a(n) = n!*sum(k=0, n\2, (-1)^k*n^(n-k)*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A292893, A356812, A356813.
%Y Cf. A320258, A356806, A356811, A356817.
%K sign
%O 0,3
%A _Seiichi Manyama_, Aug 29 2022
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