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

%I A055602 #14 May 04 2021 15:24:04
%S A055602 0,4,45,432,4200,43200,476280,5644800,71850240,979776000,14270256000,
%T A055602 221298739200,3642807168000,63465795993600,1167099373440000,
%U A055602 22596613079040000,459548157100032000,9795631769763840000
%N A055602 Number of n X n binary matrices with no 0 rows or columns and with n+1 1's.
%H A055602 Robert Israel, <a href="/A055602/b055602.txt">Table of n, a(n) for n = 1..445</a>
%F A055602 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).
%F A055602 a(n) = n*(n-1)*(n+2)*n!/4. - _Vladeta Jovovic_, Mar 25 2006
%F A055602 From _Robert Israel_, May 04 2021: (Start)
%F A055602 E.g.f.: x^2*(4-x)/(2*(1-x)^2).
%F A055602 D-finite with recurrence 4*(n-2)*a(n)-n*(4*n+3)*a(n-1)-(n-1)^2*a(n-2)=0.
%F A055602 (End)
%p A055602 f:= n -> n*(n-1)*(n+2)*n!/4:
%p A055602 map(f, [$1..30]); # _Robert Israel_, May 04 2021
%Y A055602 A diagonal of triangle A104601.
%Y A055602 Cf. A055603.
%K A055602 nonn
%O A055602 1,2
%A A055602 _Vladeta Jovovic_, Jun 01 2000
%E A055602 More terms from _David Wasserman_, Apr 28 2002