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 A293510 Number of connected minimal covers of n vertices. 20
 1, 1, 1, 4, 23, 241, 3732, 83987, 2666729, 117807298, 7217946453, 612089089261, 71991021616582, 11761139981560581, 2675674695560997301, 849270038176762472316, 376910699272413914514283, 234289022942841270608166061, 204344856617470777364053906796 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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). LINKS EXAMPLE The a(3) = 4 covers are: ((12)(13)), ((12)(23)), ((13)(23)), ((123)). 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}] CROSSREFS Cf. A030019, A046165, A048143, A275307, A283877. Sequence in context: A316083 A326501 A123637 * A234595 A327367 A303652 Adjacent sequences:  A293507 A293508 A293509 * A293511 A293512 A293513 KEYWORD nonn AUTHOR Gus Wiseman, Oct 11 2017 STATUS approved

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Last modified December 12 07:00 EST 2019. Contains 329948 sequences. (Running on oeis4.)