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%I #5 Oct 22 2024 07:37:48
%S 0,0,0,108,25200,6566400,2263917600,1070863718400,695561049469440,
%T 612326076235776000,716999439503394432000,1094463733944478334976000,
%U 2136344904330981293005056000,5240068882948994816402679398400,15901807526128013295439617984000000,58888414506334327924778872791367680000,262906951354695579633857525111586324480000
%N a(n) = (n!^2*n^(n-1)/4) * Sum_{k=4..n} A000276(k) / (n^k * (n-k)!).
%C The formula was listed in A174637 by _Vladimir Shevelev_. However, it produces a different sequence given here. Apparently, it is also related to permanents of (0,1)-matrices.
%D V. S. Shevelev, On the permanent of the stochastic (0,1)-matrices with equal row sums, Izvestia Vuzov of the North-Caucasus region, Nature sciences 1 (1997), 21-38 (in Russian).
%F a(n) = (n!^2*n^(n-1)/4) * Sum_{k=4..n} A000276(k) / (n^k * (n-k)!).
%F For n>=3, a(n) = n! * (((n-1)!/4)*A000276(n) + Sum_{k=2..n-1} (-1)^(n+k+1) * binomial(n,k) * k^(n-k) * a(k)/k!).
%Y Cf. A000276, A174637.
%K nonn
%O 1,4
%A _Max Alekseyev_, Oct 21 2024