A377246 a(n) = (n!^2*n^(n-1)/4) * Sum_{k=4..n} A000276(k) / (n^k * (n-k)!).

0, 0, 0, 108, 25200, 6566400, 2263917600, 1070863718400, 695561049469440, 612326076235776000, 716999439503394432000, 1094463733944478334976000, 2136344904330981293005056000, 5240068882948994816402679398400, 15901807526128013295439617984000000, 58888414506334327924778872791367680000, 262906951354695579633857525111586324480000

Offset: 1

Author

Max Alekseyev, Oct 21 2024

Keywords

• nonn

Comments

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.

References

• 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).

Crossrefs

Cf. A000276, A174637.

Formula

a(n) = (n!^2*n^(n-1)/4) * Sum_{k=4..n} A000276(k) / (n^k * (n-k)!).

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!).