A001866 -id:A001866 - cp's OEIS frontend

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

Vladimir Shevelev, Mar 25 2010

nonn

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

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).

Max Alekseyev, Table of n, a(n) for n = 1..100

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

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

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

Incorrect formula moved to A377246 and terms a(15) onward added by Max Alekseyev, Oct 21 2024

A174638 Number of n X n (0,1)-matrices with two 1's in each row and permanent equal to 8.

Original entry on oeis.org

0, 0, 0, 0, 0, 1350, 529200, 172872000, 58352555520, 21677788944000, 9059008787136000, 4286753834515891200, 2297335836334687948800, 1390520517156693315993600, 946759961227258909995264000

Offset: 1

Vladimir Shevelev, Mar 25 2010

nonn

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

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1967, Ch.4, 66-79.
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)

Cf. A000276, A001866, A174637, A174586.

For m >= 1, the number of n X n (0,1)-matrices with two 1's in each row with the permanent 2^m is n! * n^(n-1) / 2^m * Sum{k=2,...,n} k * n^(-k) * binomial(n,k) * d(k,m), where d(k,m) are associated Stirling numbers of the first kind (see Riordan, p. 75).

cp's OEIS Frontend

A174637 Number of n X n (0,1) matrices with two 1's in each row the permanent of which equals to 4.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

PARI

Formula

Extensions