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A174637
Number of n X n (0,1) matrices with two 1's in each row the permanent of which equals to 4.
3
0, 0, 0, 18, 2400, 325800, 52496640, 10304300160, 2458401684480, 705918026419200, 241147866161664000, 96890287539173990400, 45304089884519168102400, 24415719893124157985587200, 15035096121857624246353920000, 10496828397482345253454479360000, 8250414679239607850470753370112000
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
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
PROG
(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
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Vladimir Shevelev, Mar 25 2010
EXTENSIONS
Incorrect formula moved to A377246 and terms a(15) onward added by Max Alekseyev, Oct 21 2024
STATUS
approved