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A059087
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Triangle T(n,m) of number of labeled n-node T_0-hypergraphs with m distinct hyperedges (empty hyperedge excluded),m=0,1,...,2^n-1.
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5
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1, 1, 1, 0, 2, 3, 1, 0, 0, 12, 32, 35, 21, 7, 1, 0, 0, 12, 256, 1155, 2877, 4963, 6429, 6435, 5005, 3003, 1365, 455, 105, 15, 1, 0, 0, 0, 1120, 19040, 140616, 686476, 2565260, 7824375, 20110025, 44322135, 84658665, 141115975, 206252025, 265182375
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.
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LINKS
| V. Jovovic, Illustration of initial terms of A059087, A059088
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FORMULA
| T(n, m)=Sum_{i=0..n} s(n, i)*binomial(2^i-1, m), where s(n, i) are Stirling numbers of the first kind.
Also T(n, m)=(1/m!)*Sum_{i=0..m+1} s(m+1, i)*fallfac(2^(i-1), n). E.g.f: Sum((1+x)^(2^n-1)*ln(1+y)^n/n!, n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 19 2004
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EXAMPLE
| [1],[1,1],[0,2,3,1],[0,0,12,32,35,21,7,1],...; There are 12 labeled 3-node T_0-hypergraphs with 2 distinct hyperedges:{{3},{2}}, {{3},{2,3}}, {{2},{2,3}}, {{3},{1}}, {{3},{1,3}}, {{2},{1}}, {{2,3},{1,3}}, {{2},{1,2}}, {{2,3},{1,2}}, {{1},{1,3}}, {{1},{1,2}}, {{1,3},{1,2}}.
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CROSSREFS
| Cf. A059084-A059086, A059088, A059089.
Sequence in context: A010341 A072772 A124314 * A030373 A079343 A004566
Adjacent sequences: A059084 A059085 A059086 * A059088 A059089 A059090
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2000
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