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
Keywords
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
Programs
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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
Comments