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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). 9
1, 4, 1, 19, 7, 2, 91, 46, 16, 3, 436, 279, 115, 28, 5, 1991, 1563, 740, 221, 49, 7, 8651, 7978, 4309, 1524, 405, 75, 10, 35354, 37290, 22604, 9272, 2875, 659, 115, 13, 135617, 159948, 107584, 50058, 17840, 4866, 1042, 163, 18, 488312, 633211 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Row sums give A005785.
LINKS
FORMULA
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.
EXAMPLE
[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.
CROSSREFS
Sequence in context: A259051 A192722 A300141 * A141233 A055139 A349708
KEYWORD
nonn,tabl
AUTHOR
Vladeta Jovovic, Oct 17 2000
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)