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A049055
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Triangle read by rows, giving T(n,k) = number of k-member minimal ordered covers of a labeled n-set (n > 0, k > 0).
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2
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1, 1, 1, 2, 1, 12, 6, 1, 50, 132, 24, 1, 180, 1830, 1560, 120, 1, 602, 20460, 60960, 20520, 720, 1, 1932, 201726, 1856400, 2047920, 302400, 5040, 1, 6050, 1832292, 48550824, 155801520, 72586080, 4979520, 40320, 1, 18660, 15717750
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
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EXAMPLE
| 1; 1; 1,2; 1,12,6; 1,50,132,24; ...
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MATHEMATICA
| t[n_, k_] := Sum[ (-1)^i*Binomial[k, i]*(2^k - 1 - i)^n, {i, 0, k}]; Flatten[ Join[{1}, Table[t[n, k], {n, 1, 9}, {k, 1, n}]]] (* From Jean-François Alcover, Dec 12 2011, after Michael Somos *)
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PROG
| (PARI) {T(n, k)=sum(i=0, k, (-1)^i*binomial(k, i)*(2^k-1-i)^n)} /* Michael Somos Oct 16 2006 */
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CROSSREFS
| Row sums are A049056.
Sequence in context: A167128 A181417 A048743 * A008285 A119274 A066991
Adjacent sequences: A049052 A049053 A049054 * A049056 A049057 A049058
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KEYWORD
| nonn,tabf,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Michael Somos
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