A055602 Number of n X n binary matrices with no 0 rows or columns and with n+1 1's.

0, 4, 45, 432, 4200, 43200, 476280, 5644800, 71850240, 979776000, 14270256000, 221298739200, 3642807168000, 63465795993600, 1167099373440000, 22596613079040000, 459548157100032000, 9795631769763840000

Offset: 1

Author

Vladeta Jovovic, Jun 01 2000

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..445

Crossrefs

A diagonal of triangle A104601.

Cf. A055603.

Programs

Maple

f:= n -> n*(n-1)*(n+2)*n!/4:
map(f, [$1..30]); # Robert Israel, May 04 2021

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*binomial(n, i)*a(m, n-i, k) where a(m, n, k)=Sum_{i=0..m} (-1)^i*binomial(m, i)*binomial((m-i)*n, k).

a(n) = n*(n-1)*(n+2)*n!/4. - Vladeta Jovovic, Mar 25 2006

From Robert Israel, May 04 2021: (Start)

E.g.f.: x^2*(4-x)/(2*(1-x)^2).

D-finite with recurrence 4*(n-2)*a(n)-n*(4*n+3)*a(n-1)-(n-1)^2*a(n-2)=0.

(End)

Extensions

More terms from David Wasserman, Apr 28 2002