A174637 - OEIS

%I #17 Oct 29 2024 20:31:48

%S 0,0,0,18,2400,325800,52496640,10304300160,2458401684480,

%T 705918026419200,241147866161664000,96890287539173990400,

%U 45304089884519168102400,24415719893124157985587200,15035096121857624246353920000,10496828397482345253454479360000,8250414679239607850470753370112000

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

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

%D 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).

%H Max Alekseyev, <a href="/A174637/b174637.txt">Table of n, a(n) for n = 1..100</a>

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

%F 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

%o (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

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

%K nonn

%O 1,4

%A _Vladimir Shevelev_, Mar 25 2010

%E Incorrect formula moved to A377246 and terms a(15) onward added by _Max Alekseyev_, Oct 21 2024