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, 15035096121857624246353920000, 10496828397482345253454479360000, 8250414679239607850470753370112000

Offset: 1

Author

Vladimir Shevelev, Mar 25 2010

Keywords

• nonn

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

• Max Alekseyev, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000276, A001866, A174638, A174586, A377246.

Programs

PARI

a174637(n) = n!*(n-1)!/4 * sum(l=0,n-4, n^l/l! * sum(i=2, n-l-2, 1/i)); \\ Max Alekseyev, Oct 21 2024

Formula

a(n) = n!/4 * Sum_{l=0..n-4} binomial(n-1,l) * n^l * A000276(n-l). - Max Alekseyev, Oct 21 2024

G.f. for 4*a(n)/n!/(n-1)!: (W(-x)-ln(1+W(-x)))*(W(-x)/(1+W(-x)))^2, where W() is Lambert W-function. - Max Alekseyev, Oct 21 2024

Extensions

Incorrect formula moved to A377246 and terms a(15) onward added by Max Alekseyev, Oct 21 2024