%I #23 Oct 08 2017 17:39:41
%S 1,1,3,19,207,3691,103263,4415419,283796607,27094905451,3813398797023,
%T 786844659227419,237151202183603007,104128385332221915211,
%U 66478899089080159079583,61624041121329496987905019
%N Number of minimal ordered covers of a labeled n-set.
%H Vincenzo Librandi, <a href="/A049056/b049056.txt">Table of n, a(n) for n = 0..100</a>
%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 E.g.f.: Sum_{n>=0} (exp(x)-1)^n*exp(x*(2^n-n-1)), cf. A046165. - _Vladeta Jovovic_, Sep 01 2005
%t a[0] = 1; a[n_] := Sum[ (-1)^i*Binomial[k, i]*(2^k-1-i)^n, {k, 0, n}, {i, 0, k} ]; Table[a[n], {n, 0, 15}] (* _Jean-François Alcover_, Jan 27 2012, after _Michael Somos_ *)
%o (PARI) {a(n)=sum(k=0, n, sum(i=0, k, (-1)^i*binomial(k, i)*(2^k-1-i)^n))} /* _Michael Somos_, Oct 16 2006 */
%Y Row sums of A049055.
%K nonn,easy,nice
%O 0,3
%A _N. J. A. Sloane_, _Michael Somos_