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Search: id:A060053
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| A060053 |
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r-bicoverings of an n-set. |
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+0
23
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| 1, 0, 1, 5, 43, 518, 8186, 163356, 3988342, 116396952, 3985947805, 157783127673, 7131072006829, 364166073164914, 20827961078794845, 1323968417981743817, 92917890994442697487, 7157607311779373890120, 602043767970637640566684
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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A bicovering is r-bicovering if intersection of every two blocks contains at most one element.
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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FORMULA
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E.g.f. for number of k-block r-bicoverings of an n-set is exp(-x-1/2*x^2*y)*Sum_{i=0..inf} (1+y)^binomial(i, 2)*x^i/i!. a(n) = row sums of A060052.
Inverse binomial transform of A014500. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 22 2006
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EXAMPLE
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There are 5 r-bicoverings of a 3-set: 1 3-block bicovering {{1, 2}, {1, 3}, {2, 3}} and 4 4-block bicoverings {{1}, {2}, {3}, {1, 2, 3}}, {{2}, {3}, {1, 2}, {1, 3}}, {{1}, {3}, {1, 2}, {2, 3}}, {{1}, {2}, (1, 3}, {2, 3}}.
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CROSSREFS
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Cf. A060051, A060052, A002718, A059443, A003462, A059945-A059951.
Sequence in context: A092471 A093620 A107720 this_sequence A132691 A090470 A052895
Adjacent sequences: A060050 A060051 A060052 this_sequence A060054 A060055 A060056
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 15 2001
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