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A057963
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Triangle T(n,k) of number of minimal 2-covers of a labeled n-set that cover k points of that set uniquely (k=2,..,n).
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9
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1, 3, 3, 6, 12, 7, 10, 30, 35, 15, 15, 60, 105, 90, 31, 21, 105, 245, 315, 217, 63, 28, 168, 490, 840, 868, 504, 127, 36, 252, 882, 1890, 2604, 2268, 1143, 255, 45, 360, 1470, 3780, 6510, 7560, 5715, 2550, 511, 55, 495, 2310, 6930, 14322, 20790, 20955, 14025
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| Row sums give A000392.
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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], [3, 3], [6, 12, 7], [10, 30, 35, 15], ...; there are 90=10+30+35+15 minimal 2-covers of a labeled 5-set.
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CROSSREFS
| Cf. A035347, A057669, A057964-A057968.
Sequence in context: A110952 A025250 A094305 * A112434 A050067 A046875
Adjacent sequences: A057960 A057961 A057962 * A057964 A057965 A057966
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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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