A174637 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

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

(list; graph; refs; listen; history; text; internal format)

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

Table of n, a(n) for n=1..14.

FORMULA

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)).

CROSSREFS

Cf. A000276, A001866, A174586.

Sequence in context: A327266 A299696 A282830 * A267065 A356204 A243215

Adjacent sequences: A174634 A174635 A174636 * A174638 A174639 A174640

KEYWORD

nonn,uned

AUTHOR

Vladimir Shevelev, Mar 25 2010

STATUS

approved