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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).
4

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

%S 1,156,15,14196,2730,140,984256,283920,29120,1050,57578976,22145760,

%T 3407040,245700,6951,2994106752,1439474400,295276800,31941000,1807260,

%U 42525,142719088512,82337935680,21112291200,3045042000,258438180

%N 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).

%C Row sums give A046166.

%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], [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.

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

%K easy,nonn,tabl

%O 5,2

%A _Vladeta Jovovic_, Oct 17 2000