A293510 Number of connected minimal covers of n vertices.

1, 1, 1, 4, 23, 241, 3732, 83987, 2666729, 117807298, 7217946453, 612089089261, 71991021616582, 11761139981560581, 2675674695560997301, 849270038176762472316, 376910699272413914514283, 234289022942841270608166061, 204344856617470777364053906796

Offset: 0

Author

Gus Wiseman, Oct 11 2017

Keywords

• nonn

Comments

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).

Examples

			The a(3) = 4 covers are: ((12)(13)), ((12)(23)), ((13)(23)), ((123)).
		

Crossrefs

Cf. A030019, A046165, A048143, A275307, A283877.

Programs

Mathematica

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}];
Table[n!*SeriesCoefficient[1+Log[ser],{x,0,n}],{n,0,nn}]