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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

T(n,k) = A035348(n,k)*k! The order in which we cover the n-set is considered. - Geoffrey Critzer, Jun 28 2013

LINKS

Table of n, a(n) for n=1..39.

R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.

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-Fran├žois 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.

Sequence in context: A167128 A181417 A048743 * A276998 A222866 A008285

Adjacent sequences:  A049052 A049053 A049054 * A049056 A049057 A049058

KEYWORD

nonn,tabl,easy,nice

AUTHOR

N. J. A. Sloane, Michael Somos

STATUS

approved

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Last modified November 16 17:25 EST 2019. Contains 329201 sequences. (Running on oeis4.)