A055603 Number of n X n binary matrices with no zero rows or columns and with n+2 ones.

0, 1, 90, 2248, 43000, 755100, 13003620, 226262400, 4037765760, 74481120000, 1425927888000, 28389466828800, 588245898240000, 12685887076262400, 284623499160000000, 6639289429893120000, 160886197351047168000, 4046412223559946240000, 105527367894862577664000

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Formula

Number of m X n binary matrices with no zero rows or columns and with k=0..m*n ones is Sum_{i=0..n} (-1)^i*C(n, i)*a(m, n-i, k) where a(m, n, k)=Sum_{i=0..m} (-1)^i*C(m, i)*C((m-i)*n, k).

a(n) = n*(n-1)*(9*n^4+42*n^3+7*n^2-122*n-120)*n!/576. - Vladeta Jovovic, Mar 25 2006

Crossrefs

A diagonal of triangle A104601.

Cf. A055602.

Sequence in context: A065951 A257040 A008393 * A210090 A109124 A013359

Adjacent sequences: A055600 A055601 A055602 * A055604 A055605 A055606

Keyword

nonn

Author

Vladeta Jovovic, Jun 01 2000

Extensions

More terms from Vaclav Kotesovec, Jul 12 2018

Status

approved