A057965 Triangle T(n,k) of number of minimal 4-covers of a labeled n-set that cover k points of that set uniquely (k=4,..,n).

1, 55, 10, 1815, 660, 65, 46585, 25410, 5005, 350, 1024870, 745360, 220220, 30800, 1701, 20292426, 18447660, 7267260, 1524600, 168399, 7770, 372027810, 405848520, 199849650, 55902000, 9261945, 854700, 34105, 6430766430

Offset: 4

Author

Vladeta Jovovic, Oct 17 2000

Keywords

• easy
• nonn
• tabl

Comments

Row sums give A016111.

Examples

			[1], [55, 10], [1815, 660, 65], [46585, 25410, 5005, 350], ...; there are 1815 minimal 4-covers of a labeled 6-set that cover 4 points of that set uniquely.
		

Links

• Eric Weisstein's World of Mathematics, Minimal cover

Crossrefs

Cf. A035347, A057669, A057963, A057964, A057966, A057967(unlabeled case), A057968.

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.