A057966 Triangle T(n,k) of number of minimal 5-covers of a labeled n-set that cover k points of that set uniquely (k=5,..,n).

1, 156, 15, 14196, 2730, 140, 984256, 283920, 29120, 1050, 57578976, 22145760, 3407040, 245700, 6951, 2994106752, 1439474400, 295276800, 31941000, 1807260, 42525, 142719088512, 82337935680, 21112291200, 3045042000, 258438180

Offset: 5

Author

Vladeta Jovovic, Oct 17 2000

Keywords

• easy
• nonn
• tabl

Comments

Row sums give A046166.

Examples

			[1], [156, 15], [14196, 2730, 140], [984256, 283920, 29120, 1050], ...; there are 15 minimal 5-covers of a labeled 6-set that cover 6 points of that set uniquely.
		

Links

• Eric Weisstein's World of Mathematics, Minimal cover

Crossrefs

Cf. A035347, A057669, A057963-A057965, A057967, A057968(unlabeled case).

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.