A057964 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).

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

Offset: 3

Author

Vladeta Jovovic, Oct 17 2000

Keywords

• easy
• nonn
• tabl

Comments

Row sums give A003468.

Examples

			[1], [16, 6], [160, 120, 25], [1280, 1440, 600, 90], ...; There are 305=160+120+25 minimal 3-covers of a labeled 5-set.
		

Links

• Eric Weisstein's World of Mathematics, Minimal cover

Crossrefs

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