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Number of n X n binary matrices with no zero rows or columns and with n+2 ones.
4

%I #9 Jul 12 2018 05:38:46

%S 0,1,90,2248,43000,755100,13003620,226262400,4037765760,74481120000,

%T 1425927888000,28389466828800,588245898240000,12685887076262400,

%U 284623499160000000,6639289429893120000,160886197351047168000,4046412223559946240000,105527367894862577664000

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

%F 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).

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

%Y A diagonal of triangle A104601.

%Y Cf. A055602.

%K nonn

%O 1,3

%A _Vladeta Jovovic_, Jun 01 2000

%E More terms from _Vaclav Kotesovec_, Jul 12 2018