A049055 Triangle read by rows, giving T(n,k) = number of k-member minimal ordered covers of a labeled n-set (1 <= k <= n).

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

Offset

1,3

Links

Table of n, a(n) for n=1..45.

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

Adjacent sequences: A049052 A049053 A049054 * A049056 A049057 A049058

Keyword

nonn,tabl,easy,nice

Author

N. J. A. Sloane, Michael Somos

Status

approved