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Search: id:A060492
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| A060492 |
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Triangle T(n,k) of k-block ordered tricoverings of an unlabeled n-set (n >= 3, k >= 4). |
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5
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| 4, 60, 120, 13, 375, 3030, 9030, 5040, 28, 1392, 24552, 207900, 838320, 1345680, 362880, 50, 4020, 130740, 2208430, 20334720, 101752560, 257065200, 261122400, 46569600, 80, 9960, 551640, 16365410, 274814760, 2709457128, 15812198640
(list; graph; listen)
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OFFSET
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3,1
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COMMENT
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A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.
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FORMULA
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E.g.f. for ordered k-block tricoverings of an unlabeled n-set is exp(-x+x^2/2+x^3/3*y/(1-y))*Sum_{k=0..inf}1/(1-y)^binomial(k, 3)*exp(-x^2/2*1/(1-y)^n)*x^k/k!.
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EXAMPLE
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[4, 60, 120], [13, 375, 3030, 9030, 5040], [28, 1392, 24552, 207900, 838320, 1345680, 362880], [50, 4020, 130740, 2208430, 20334720, 101752560, 257065200, 261122400, 46569600], [80, 9960, 551640, 16365410, 274814760, 2709457128, 15812198640, 52897521600, 91945022400, 64778313600, 8043235200], ...; there are 184 ordered tricoverings of an unlabeled 3-set: 4 4-block, 60 5-block and 120 6-block tricoverings (cf. A060491).
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CROSSREFS
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Cf. A006095, A060483-A060490, (row sums) A060491, A060090-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951.
Sequence in context: A026586 A058173 A074835 this_sequence A112041 A002060 A007220
Adjacent sequences: A060489 A060490 A060491 this_sequence A060493 A060494 A060495
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 20 2001
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