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A094544
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Triangle of a(n,m) = number of m-member minimal T_0-covers of an n-set (n >= 0, 0<= m <=n).
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3
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1, 0, 1, 0, 0, 1, 0, 0, 3, 1, 0, 0, 0, 16, 1, 0, 0, 0, 120, 55, 1, 0, 0, 0, 480, 1650, 156, 1, 0, 0, 0, 840, 34650, 13650, 399, 1, 0, 0, 0, 0, 554400, 873600, 89376, 960, 1, 0, 0, 0, 0, 6985440, 45208800, 14747040, 514080, 2223, 1, 0, 0, 0, 0, 69854400, 1989187200
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OFFSET
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0,9
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COMMENTS
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A cover of a set is a T_0-cover if for every two distinct points of the set there exists a member (block) of the cover containing one but not the other point.
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LINKS
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FORMULA
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a(n, m) = n!/m!*binomial(2^m-m-1, n-m).
E.g.f.: Sum_{n>=0} y^n*(1+y)^(2^n-n-1)*x^n/n!.
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EXAMPLE
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1;
0, 1;
0, 0, 1;
0, 0, 3, 1;
0, 0, 0, 16, 1;
0, 0, 0, 120, 55, 1;
0, 0, 0, 480, 1650, 156, 1;
...
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MATHEMATICA
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Flatten[Table[n!/m! Binomial[2^m-m-1, n-m], {n, 0, 10}, {m, 0, n}]] (* Harvey P. Dale, Jan 16 2012 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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