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

0,4

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

Table of n, a(n) for n=0..18.

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