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Search: id:A059085
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| A059085 |
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Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge included). |
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+0
5
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| 2, 4, 12, 216, 64152, 4294320192, 18446744009290559040, 340282366920938463075992982635439125760, 115792089237316195423570985008687907843742078391854287068422946583140399879680
(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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LINKS
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V. Jovovic, Illustration of initial terms of A059084, A059085
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FORMULA
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Row sums of A059084.
a(n)=Sum_{k=0..n} stirling1(n, k)*2^(2^k).
E.g.f.: Sum(2^(2^n)*ln(1+x)^n/n!, n=0..infinity) = Sum(ln(2)^n*(1+x)^(2^n)/n!, n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 10 2004
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EXAMPLE
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There are 216 labeled 3-node T_0-hypergraphs without multiple hyperedges (empty hyperedge included): 12 with 2 hyperedges, 44 with 3 hyperedges,67 with 4 hyperedges, 56 with 5 hyperedges, 28 with 6 hyperedges, 8 with 7 hyperedges and 1 with 8 hyperedges.
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MAPLE
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with(combinat): for n from 0 to 15 do printf(`%d, `, sum(stirling1(n, k)*2^(2^k), k=0..n)) od:
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CROSSREFS
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Cf. A059084, A059086, A059087-A059089.
Sequence in context: A062000 A053040 A154734 this_sequence A030064 A109928 A023640
Adjacent sequences: A059082 A059083 A059084 this_sequence A059086 A059087 A059088
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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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