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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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2, 3, 27, 18209, 2369751602470, 5960531437867327674538684858601298, 479047836152505670895481842190009123676957243077039687942939196956404642582185242435050
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
| Column sums of A059087.
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
| 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
| 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
| Cf. A059084-A059088.
Sequence in context: A126203 A126655 A132533 * A098812 A073049 A037320
Adjacent sequences: A059086 A059087 A059088 * A059090 A059091 A059092
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KEYWORD
| easy,nonn
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AUTHOR
| Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 24 2001
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