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Search: id:A055599
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| A055599 |
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Triangle T(n,k) giving the number of n X n binary matrices with no zero rows or columns and with k=0..n^2 ones. |
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4
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| 0, 1, 0, 0, 2, 4, 1, 0, 0, 0, 6, 45, 90, 78, 36, 9, 1, 0, 0, 0, 0, 24, 432, 2248, 5776, 9066, 9696, 7480, 4272, 1812, 560, 120, 16, 1, 0, 0, 0, 0, 0, 120, 4200, 43000, 222925, 727375, 1674840, 2913100, 3995100, 4441200, 4073100, 3114140, 1994550
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OFFSET
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1,5
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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*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).
G.f. for n-th row: Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*((1+x)^k-1)^n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 04 2003
E.g.f.: Sum(((1+y)^n-1)^n*exp((1-(1+y)^n)*x)*x^n/n!,n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 24 2008
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EXAMPLE
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For m=n=3 we get T(3,k)=C(9,k)-6*C(6,k)+9*C(4,k)+6*C(3,k)-18*C(2,k)+9*C(1,k)-C(0,k) giving the batch [0,0,0,6,45,90,78,36,9,1].
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CROSSREFS
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Row sums give A048291.
Sequence in context: A012710 A009512 A163259 this_sequence A115407 A010586 A070678
Adjacent sequences: A055596 A055597 A055598 this_sequence A055600 A055601 A055602
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 01 2000
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