OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..445
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)
MAPLE
f:= n -> n*(n-1)*(n+2)*n!/4:
map(f, [$1..30]); # Robert Israel, May 04 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Jun 01 2000
EXTENSIONS
More terms from David Wasserman, Apr 28 2002
STATUS
approved