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Search: id:A059088
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| A059088 |
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Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge excluded). |
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+0
3
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| 1, 2, 6, 108, 32076, 2147160096, 9223372004645279520, 170141183460469231537996491317719562880, 57896044618658097711785492504343953921871039195927143534211473291570199939840
(list; graph; listen)
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OFFSET
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0,2
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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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LINKS
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Illustration of initial terms of A059087, A059088
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FORMULA
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Row sums of A059087. a(n)=A059085(n)/2.
a(n)=A059085(n)/2=Sum_{k=0..n} stirling1(n, k)*2^((2^k)-1).
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EXAMPLE
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There are 108 labeled 3-node T_0-hypergraphs without multiple hyperedges (empty hyperedge excluded): 12 with 2 hyperedges, 32 with 3 hyperedges,35 with 4 hyperedges, 21 with 5 hyperedges, 7 with 6 hyperedges and 1 with 7 hyperedges.
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MAPLE
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with(combinat): for n from 0 to 15 do printf(`%d, `, (1/2)*sum(stirling1(n, k)*2^(2^k), k= 0..n)) od:
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CROSSREFS
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Cf. A059084-A059087, A059089.
Sequence in context: A123257 A054247 A099790 this_sequence A057771 A056164 A156500
Adjacent sequences: A059085 A059086 A059087 this_sequence A059089 A059090 A059091
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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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