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A059089
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Number of labeled T_0-hypergraphs with n distinct hyperedges (empty hyperedge excluded).
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7
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OFFSET
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0,1
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COMMENTS
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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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LINKS
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FORMULA
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a(n) = Sum_{k = 0..n} (-1)^(n-k)*A059086(k); a(n) = (1/n!)*Sum_{k = 0..n+1} stirling1(n+1, k)*floor(( 2^(k-1))!*exp(1)).
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EXAMPLE
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a(2)=27; There are 27 labeled T_0-hypergraphs with 2 distinct hyperedges (empty hyperedge excluded): 3 2-node hypergraphs, 12 3-node hypergraphs and 12 4-node hypergraphs.
a(3) = (1/3!)*(-6*[1!*e]+11*[2!*e]-6*[4!*e]+[8!*e]) = (1/3!)*(-6*2+11*5-6*65+109601) = 18209, 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+1, k)*floor((2^(k-1))!*exp(1)), k=0..n+1)) od:
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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