login
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).
4

%I #5 May 10 2013 12:44:32

%S 1,16,6,160,120,25,1280,1440,600,90,8960,13440,8400,2520,301,57344,

%T 107520,89600,40320,9632,966,344064,774144,806400,483840,173376,34776,

%U 3025,1966080,5160960,6451200,4838400,2311680,695520,121000,9330

%N 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).

%C Row sums give A003468.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalCover.html">Minimal cover</a>

%F 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.

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

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

%K easy,nonn,tabl

%O 3,2

%A _Vladeta Jovovic_, Oct 17 2000