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A055602
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Number of n X n binary matrices with no 0 rows or columns and with n+1 1's.
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9
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0, 4, 45, 432, 4200, 43200, 476280, 5644800, 71850240, 979776000, 14270256000, 221298739200, 3642807168000, 63465795993600, 1167099373440000, 22596613079040000, 459548157100032000, 9795631769763840000
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OFFSET
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1,2
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LINKS
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FORMULA
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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).
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)
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MAPLE
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f:= n -> n*(n-1)*(n+2)*n!/4:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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