A174637 Number of n X n (0,1) matrices with two 1's in each row the permanent of which equals to 4.

0, 0, 0, 18, 2400, 325800, 52496640, 10304300160, 2458401684480, 705918026419200, 241147866161664000, 96890287539173990400, 45304089884519168102400, 24415719893124157985587200

Offset

1,4

Comments

If a (0,1) matrix with two 1's in each row has positive permanent, then it equals to a power of 2.

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).

Links

Table of n, a(n) for n=1..14.

Formula

Explicit formula: a(n) = (n!^2*n^(n-1)/4)*Sum_{k=4..n}n^{-k)*(n-k)!^(-1)*A000276(k); recursion: a(2)=0, for n>=3, a(n) = n!*(((n-1)!/4)*A000276(n)+Sum_{k=2..n-1}(-1)^(n+k+1)*C(n,k)*k^(n-k)*((k!)^(-1))*a(k)).

Crossrefs

Cf. A000276, A001866, A174586.

Sequence in context: A327266 A299696 A282830 * A267065 A356204 A243215

Adjacent sequences: A174634 A174635 A174636 * A174638 A174639 A174640

Keyword

nonn,uned

Author

Vladimir Shevelev, Mar 25 2010

Status

approved