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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).
5

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

%S 1,55,10,1815,660,65,46585,25410,5005,350,1024870,745360,220220,30800,

%T 1701,20292426,18447660,7267260,1524600,168399,7770,372027810,

%U 405848520,199849650,55902000,9261945,854700,34105,6430766430

%N 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).

%C Row sums give A016111.

%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], [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.

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

%K easy,nonn,tabl

%O 4,2

%A _Vladeta Jovovic_, Oct 17 2000