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Search: id:A059586
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| A059586 |
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Number of labeled T_0-hypergraphs with n hyperedges (empty hyperedges and multiple hyperedges included). |
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+0
3
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| 2, 5, 35, 18301, 2369751675482, 5960531437867327674550533616796025, 479047836152505670895481842190009123676957243077039723706127824160370689849840668444493
(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(3) = (1/3!) * (2 * [2! * e] + 3 * [4! * e] + [8! * e]) = (1/3!) * (2 * 5 + 3 * 65 + 109601) = 18301, where [k! * e] := floor(k! * exp(1)).
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MAPLE
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with(combinat): Digits := 1000: f := n->(1/n!)*sum(abs(stirling1(n, i))*floor((2^i)!*exp(1)), i=0..n): for n from 0 to 8 do printf(`%d, `, f(n)) od:
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CROSSREFS
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Cf. A000522, A059086, A059584, A059585.
Sequence in context: A000659 A063443 A133473 this_sequence A086832 A111491 A086218
Adjacent sequences: A059583 A059584 A059585 this_sequence A059587 A059588 A059589
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic, Goran Kilibarda (vladeta(AT)Eunet.yu), Jan 23 2001
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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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