%I #25 Feb 18 2021 09:22:52
%S 1,1,2,1,12,6,1,50,132,24,1,180,1830,1560,120,1,602,20460,60960,20520,
%T 720,1,1932,201726,1856400,2047920,302400,5040,1,6050,1832292,
%U 48550824,155801520,72586080,4979520,40320,1,18660,15717750,1144994760,10006131240,13069123200,2767474080,91082880,362880
%N Triangle read by rows, giving T(n,k) = number of k-member minimal ordered covers of a labeled n-set (1 <= k <= n).
%H R. J. Clarke, <a href="http://dx.doi.org/10.1016/0012-365X(90)90146-9">Covering a set by subsets</a>, Discrete Math., 81 (1990), 147-152.
%F T(n,k) = A035348(n,k)*k!, the order in which we cover the n-set is considered. - _Geoffrey Critzer_, Jun 28 2013
%e Triangle starts
%e 1;
%e 1, 2;
%e 1, 12, 6;
%e 1, 50, 132, 24;
%e ...
%t 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_ *)
%o (PARI) {T(n, k)=sum(i=0, k, (-1)^i*binomial(k, i)*(2^k-1-i)^n)} /* _Michael Somos_, Oct 16 2006 */
%Y Row sums are A049056.
%Y Cf. A035348.
%K nonn,tabl,easy,nice
%O 1,3
%A _N. J. A. Sloane_, _Michael Somos_