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%I #4 Oct 20 2017 15:41:57
%S 1,1,1,4,23,241,3732,83987,2666729,117807298,7217946453,612089089261,
%T 71991021616582,11761139981560581,2675674695560997301,
%U 849270038176762472316,376910699272413914514283,234289022942841270608166061,204344856617470777364053906796
%N Number of connected minimal covers of n vertices.
%C A cover of a finite set S is a finite set of finite nonempty sets with union S. A cover is minimal if removing any edge results in a cover of strictly fewer vertices. A cover is connected if it is connected as a hypergraph or clutter. Note that minimality is with respect to covering rather than to connectedness (cf. A030019).
%e The a(3) = 4 covers are: ((12)(13)), ((12)(23)), ((13)(23)), ((123)).
%t nn=30;ser=Sum[(1+Sum[Binomial[n,i]*StirlingS2[i,k]*(2^k-k-1)^(n-i),{k,2,n},{i,k,n}])*x^n/n!,{n,0,nn}];
%t Table[n!*SeriesCoefficient[1+Log[ser],{x,0,n}],{n,0,nn}]
%Y Cf. A030019, A046165, A048143, A275307, A283877.
%K nonn
%O 0,4
%A _Gus Wiseman_, Oct 11 2017
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