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Search: id:A059086
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| A059086 |
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Number of labeled T_0-hypergraphs with n distinct hyperedges (empty hyperedge included). |
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+0
6
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| 2, 5, 30, 18236, 2369751620679, 5960531437867327674541054610203768, 47904783615250567089548184219000912367695724307703969390347063482373231712087010\ 1036348
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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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FORMULA
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a(n) = (1/n!)*Sum_{k = 0..n} stirling1(n, k)*floor((2^k)!*exp(1)).
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EXAMPLE
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a(2)=30; There are 30 labeled T_0-hypergraphs with 2 distinct hyperedges (empty hyperedge included): 1 1-node hypergraph, 5 2-node hypergraphs, 12 3-node hypergraphs and 12 4-node hypergraphs.
a(3) = (1/3!)*(2*[2!*e]-3*[4!*e]+[8!*e]) = (1/3!)*(2*5-3*65+109601) = 18236, where [k!*e] := floor (k!*exp(1)).
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MAPLE
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with(combinat): Digits := 1000: for n from 0 to 8 do printf(`%d, `, (1/n!)*sum(stirling1(n, k)*floor((2^k)!*exp(1)), k=0..n)) od:
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CROSSREFS
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Column sums of A059084.
Cf. A059084, A059085, A059087-A059089.
Sequence in context: A129951 A127298 A000133 this_sequence A107389 A077483 A119242
Adjacent sequences: A059083 A059084 A059085 this_sequence A059087 A059088 A059089
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KEYWORD
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easy,nonn
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AUTHOR
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Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 24 2001
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