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Search: id:A094544
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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
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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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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REFERENCES
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G. Kilibarda and V. Jovovic, "Enumeration of some classes of T_0-hypergraphs", in preparation, 2004.
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LINKS
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Eric Weisstein's World of Mathematics, Minimal Cover.
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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(y^n*(1+y)^(2^n-n-1)*x^n/n!, n=0..infinity).
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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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CROSSREFS
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Cf. A035348, A046165, A094545(row sums), A094546(column sums).
Sequence in context: A099725 A128208 A144209 this_sequence A062734 A117389 A122083
Adjacent sequences: A094541 A094542 A094543 this_sequence A094545 A094546 A094547
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Goran Kilibarda, Vladeta Jovovic (vladeta(AT)Eunet.yu), May 08 2004
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