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%I #7 Mar 08 2023 13:46:29
%S 0,0,0,18,2400,325800,52496640,10304300160,2458401684480,
%T 705918026419200,241147866161664000,96890287539173990400,
%U 45304089884519168102400,24415719893124157985587200
%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).
%F 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)).
%Y Cf. A000276, A001866, A174586.
%K nonn,uned
%O 1,4
%A _Vladimir Shevelev_, Mar 25 2010
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