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A057967
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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).
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4
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1, 3, 1, 10, 5, 2, 30, 21, 11, 3, 83, 75, 49, 18, 5, 208, 231, 177, 84, 30, 6, 495, 636, 554, 318, 143, 42, 9, 1101, 1603, 1540, 1023, 543, 210, 62, 11, 2327, 3737, 3907, 2904, 1759, 822, 311, 82, 15, 4685, 8163, 9153, 7470, 5012, 2706, 1219, 423, 111, 18, 9041
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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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, ...)
+ 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.
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EXAMPLE
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[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.
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CROSSREFS
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Cf. A001752, A056885, A057222, A057223, A057524, A057669, A057963, A057964, A057965(labeled case), A057966, A057968.
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KEYWORD
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AUTHOR
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STATUS
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approved
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