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

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

Offset: 1

Author

Vladimir Shevelev, Mar 25 2010

Keywords

• nonn

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

• 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)

Crossrefs

Cf. A000276, A001866, A174637, A174586.

Formula

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).