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A055602 Number of n X n binary matrices with no 0 rows or columns and with n+1 1's. 9
0, 4, 45, 432, 4200, 43200, 476280, 5644800, 71850240, 979776000, 14270256000, 221298739200, 3642807168000, 63465795993600, 1167099373440000, 22596613079040000, 459548157100032000, 9795631769763840000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
A diagonal of triangle A104601.
Cf. A055603.
Sequence in context: A343904 A117644 A232729 * A346629 A073565 A039657
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Jun 01 2000
EXTENSIONS
More terms from David Wasserman, Apr 28 2002
STATUS
approved

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Last modified March 3 06:28 EST 2024. Contains 370499 sequences. (Running on oeis4.)