Search: id:A057969
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%I A057969
%S A057969 1,5,24,115,551,2542,11193,46547,182164,670476,2325506,7624434,
%T A057969 23716419,70253721,198905506,540079754,1410786483,3555443969,
%U A057969 8667153126,20484365167,47037898503,105143200252,229178029000
%N A057969 5 x n binary matrices without unit columns up to row and column permutations.
%C A057969 A unit column of a binary matrix is a column with only one 1. First differences 
               of a(n) give number of minimal 5-covers of an unlabeled n-set that 
               cover 5 points of that set uniquely (if offset is 5).
%H A057969 <a href="a56885.pdf">The number of minimal covers of an unlabeled n-set 
               that cover k points of that set uniquely</a>
%H A057969 <a href="a057972.PDF">Number of binary matrices with fixed number of 
               unit columns up to row and column permutations</a>
%F A057969 a(n)=(1/5!)*(Z(S_n; 27, 27, ...) + 10*Z(S_n; 13, 27, 13, 27, ...) + 15*Z(S_n; 
               7, 27, 7, 27, ...) + 20*Z(S_n; 6, 6, 27, 6, 6, 27, ...) + 20*Z(S_n; 
               4, 6, 13, 6, 4, 27, 4, 6, 13, 6, 4, 27, ...) + 30*Z(S_n; 3, 7, 3, 
               27, 3, 7, 3, 27, ...) + 24*Z(S_n; 2, 2, 2, 2, 27, 2, 2, 2, 2, 27, 
               ...)), where Z(S_n; x_1, x_2, ..., x_n) is cycle index of symmetric 
               group S_n of degree n. G.f. : 1/120*(1/(1 - x^1)^27 + 10/(1 - x^1)^13/
               (1 - x^2)^7 + 15/(1 - x^1)^7/(1 - x^2)^10 + 20/(1 - x^1)^6/(1 - x^3)^7 
               + 20/(1 - x^1)^4/(1 - x^2)^1/(1 - x^3)^3/(1 - x^6)^2 + 30/(1 - x^1)^3/
               (1 - x^2)^2/(1 - x^4)^5 + 24/(1 - x^1)^2/(1 - x^5)^5).
%Y A057969 Cf. A001752, A056885, A057222, A057223, A057524, A057669, A057963-A057968, 
               A057970-A057972.
%Y A057969 Sequence in context: A141223 A140766 A026388 this_sequence A004254 A086347 
               A026707
%Y A057969 Adjacent sequences: A057966 A057967 A057968 this_sequence A057970 A057971 
               A057972
%K A057969 nonn
%O A057969 0,2
%A A057969 Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 20 2000

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