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%I A057968 #8 May 10 2013 12:44:32
%S A057968 1,4,1,19,7,2,91,46,16,3,436,279,115,28,5,1991,1563,740,221,49,7,8651,
%T A057968 7978,4309,1524,405,75,10,35354,37290,22604,9272,2875,659,115,13,
%U A057968 135617,159948,107584,50058,17840,4866,1042,163,18,488312,633211
%N A057968 Triangle T(n,k) of numbers of minimal 5-covers of an unlabeled n+5-set that cover k points of that set uniquely (k=5,..,n+5).
%C A057968 Row sums give A005785.
%H A057968 <a href="/A056885/a056885.pdf">More information</a>
%F A057968 T(n, k)=b(n, k)-b(n-1, k); b(n, k)=coefficient of x^k in (x^5/5!)*(Z(S_n; 27+5*x, 27+5*x^2, ...)+10*Z(S_n; 13+3*x, 27+5*x^2, 13+3*x^3, 27+5*x^4, ...)+15*Z(S_n; 7+x, 27+5*x^2, 7+x^3, 27+5*x^4, ...)+20*Z(S_n; 6+2*x, 6+2*x^2, 27+5*x^3, 6+2*x^4, 6+2*x^5, 27+5*x^6, ...)+20*Z(S_n; 4, 6+2*x^2, 13+3*x^3, 6+2*x^4, 4, 27+5*x^6, 4, 6+2*x^8, 13+3*x^9, 6+2*x^10, 4, 27+5*x^12, ...)+30*Z(S_n; 3+x, 7+x^2, 3+x^3, 27+5*x^4, 3+x^5, 7+x^6, 3+x^7, 27+5*x^8, ...)+24*Z(S_n; 2, 2, 2, 2, 27+5*x^5, 2, 2, 2, 2, 27+5*x^10, ...)), where Z(S_n; x_1, x_2, ..., x_n) is cycle index of symmetric group S_n of degree n.
%e A057968 [1], [4, 1], [19, 7, 2], [91, 46, 16, 3], [436, 279, 115, 28, 5], ...; there are 46 minimal 5-covers of an unlabeled 8-set that cover 6 points of that set uniquely.
%Y A057968 Cf. A001752, A056885, A057222, A057223, A057524, A057669, A057963, A057964, A057965, A057966(labeled case), A057967.
%K A057968 nonn,tabl
%O A057968 0,2
%A A057968 _Vladeta Jovovic_, Oct 17 2000

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