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%I M3117 #32 Oct 21 2023 19:51:53
%S 0,3,28,210,1506,10871,80592,618939,4942070,41076508,355372524,
%T 3198027157,29905143464,290243182755,2920041395248,30414515081650,
%U 327567816748638,3643600859114439,41809197852127240,494367554679088923,6017481714095327410
%N Number of minimal covers of an n-set that have exactly one point which appears in more than one set in the cover.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Robert Israel, <a href="/A003466/b003466.txt">Table of n, a(n) for n = 2..510</a>
%H T. Hearne and C. G. Wagner, <a href="http://dx.doi.org/10.1016/0012-365X(73)90141-6">Minimal covers of finite sets</a>, Discr. Math. 5 (1973), 247-251.
%F a(n) = n * Sum_{k=1..n-1} (2^k-k-1) * S2(n-1,k) where S2(n,k) are the Stirling numbers of the second kind. - _Sean A. Irvine_, May 20 2015
%F a(n) = n * (A001861(n-1) - A005493(n-2) - A000110(n-1)). - _Robert Israel_, May 21 2015
%p seq(n*add((2^k-k-1)*Stirling2(n-1,k),k=1..n-1), n = 2 .. 30); # _Robert Israel_, May 21 2015
%t nn = 20; Range[0, nn]! CoefficientList[Series[Sum[ (Exp[x] - 1)^n/n! (2^n - n - 1) x, {n, 0, nn}], {x, 0, nn}], x] (* _Geoffrey Critzer_, Feb 18 2017 *)
%t a[2]=0;a[3]=3;a[4]=28;a[n_]:=n*Sum[(2^k-k-1)* StirlingS2[n-1,k], {k,1,n-1}];Table[a[n],{n,2,22}] (* _Indranil Ghosh_, Feb 20 2017 *)
%Y Cf. A046165.
%Y Column k=1 of A282575.
%K nonn
%O 2,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, May 20 2015
%E Title clarified by _Geoffrey Critzer_, Feb 18 2017
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