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

1,6

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)

Links

Table of n, a(n) for n=1..15.

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).

Crossrefs

Cf. A000276, A001866, A174637, A174586.

Sequence in context: A260542 A307218 A278383 * A154375 A243132 A349070

Adjacent sequences: A174635 A174636 A174637 * A174639 A174640 A174641

Keyword

nonn

Author

Vladimir Shevelev, Mar 25 2010

Status

approved