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A057967 Triangle T(n,k) of numbers of minimal 4-covers of an unlabeled n+4-set that cover k points of that set uniquely (k=4,..,n+4).

%I A057967 #8 May 10 2013 12:44:32
%S A057967 1,3,1,10,5,2,30,21,11,3,83,75,49,18,5,208,231,177,84,30,6,495,636,
%T A057967 554,318,143,42,9,1101,1603,1540,1023,543,210,62,11,2327,3737,3907,
%U A057967 2904,1759,822,311,82,15,4685,8163,9153,7470,5012,2706,1219,423,111,18,9041
%N A057967 Triangle T(n,k) of numbers of minimal 4-covers of an unlabeled n+4-set that cover k points of that set uniquely (k=4,..,n+4).
%C A057967 Row sums give A005784.
%H A057967 <a href="/A056885/a056885.pdf">More information</a>
%F A057967 T(n, k) = b(n, k)-b(n-1, k); b(n, k) = coefficient of x^k in x^4/24*(Z(S_n; 12 + 4*x, 12 + 4*x^2, ...) + 8*Z(S_n; 3 + x, 3 + x^2, 12 + 4*x^3, 3 + x^4, 3 + x^5, 12 + 4*x^6, ...) + 6*Z(S_n; 6 + 2*x, 12 + 4*x^2, 6 + 2*x^3, 12 + 4*x^4, ...)
%F A057967 + 3*Z(S_n; 4, 12 + 4*x^2, 4, 12 + 4*x^4, ...) + 6*Z(S_n; 2, 4, 2, 12 + 4*x^4, 2, 4, 2, 12 + 4*x^8, ...)), where Z(S_n; x_1, x_2, ..., x_n) is the cycle index of the symmetric group S_n of degree n.
%e A057967 [1], [3, 1], [10, 5, 2], [30, 21, 11, 3], [83, 75, 49, 18], ...; there are 5 minimal 4-covers of an unlabeled 6-set that cover 5 points of that set uniquely.
%Y A057967 Cf. A001752, A056885, A057222, A057223, A057524, A057669, A057963, A057964, A057965(labeled case), A057966, A057968.
%K A057967 nonn,tabl
%O A057967 0,2
%A A057967 _Vladeta Jovovic_, Oct 17 2000