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A049055 Triangle read by rows, giving T(n,k) = number of k-member minimal ordered covers of a labeled n-set (1 <= k <= n). 2
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, 1144994760, 10006131240, 13069123200, 2767474080, 91082880, 362880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
FORMULA
T(n,k) = A035348(n,k)*k!, the order in which we cover the n-set is considered. - Geoffrey Critzer, Jun 28 2013
EXAMPLE
Triangle starts
1;
1, 2;
1, 12, 6;
1, 50, 132, 24;
...
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}]]] (* Jean-François Alcover, Dec 12 2011, after Michael Somos *)
PROG
(PARI) {T(n, k)=sum(i=0, k, (-1)^i*binomial(k, i)*(2^k-1-i)^n)} /* Michael Somos, Oct 16 2006 */
CROSSREFS
Row sums are A049056.
Cf. A035348.
Sequence in context: A342430 A181417 A048743 * A276998 A222866 A342587
KEYWORD
nonn,tabl,easy,nice
AUTHOR
STATUS
approved

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Last modified March 28 16:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)