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A057964
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Triangle T(n,k) of number of minimal 3-covers of a labeled n-set that cover k points of that set uniquely (k=3,..,n).
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4
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1, 16, 6, 160, 120, 25, 1280, 1440, 600, 90, 8960, 13440, 8400, 2520, 301, 57344, 107520, 89600, 40320, 9632, 966, 344064, 774144, 806400, 483840, 173376, 34776, 3025, 1966080, 5160960, 6451200, 4838400, 2311680, 695520, 121000, 9330
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| Row sums give A003468.
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LINKS
| Eric Weisstein's World of Mathematics, Minimal cover
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FORMULA
| Number of minimal m-covers of a labeled n-set that cover k points of that set uniquely is C(n, k)*S(k, m)*(2^m-m-1)^(n-k), where S(k, m) are Stirling numbers of the second kind.
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EXAMPLE
| [1], [16, 6], [160, 120, 25], [1280, 1440, 600, 90], ...; There are 305=160+120+25 minimal 3-covers of a labeled 5-set.
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CROSSREFS
| Cf. A035347, A057669 (unlabeled case), A057963, A057965-A057968.
Sequence in context: A161884 A166210 A141078 * A131030 A070580 A028579
Adjacent sequences: A057961 A057962 A057963 * A057965 A057966 A057967
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 17 2000
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