A369196 Number of labeled loop-graphs with n vertices and at most as many edges as covered vertices.

1, 2, 7, 39, 320, 3584, 51405, 900947, 18661186, 445827942, 12062839691, 364451604095, 12157649050827, 443713171974080, 17583351295466338, 751745326170662049, 34485624653535808340, 1689485711682987916502, 88030098291829749593643, 4860631073631586486397141

Offset: 0

Author

Gus Wiseman, Jan 17 2024

Keywords

• nonn

Examples

			The a(0) = 1 through a(2) = 7 loop-graphs:
  {}  {}     {}
      {{1}}  {{1}}
             {{2}}
             {{1,2}}
             {{1},{2}}
             {{1},{1,2}}
             {{2},{1,2}}
		

Crossrefs

The version counting all vertices is A066383, without loops A369192.

The loopless case is A369193, with case of equality A367862.

The covering case is A369194, connected A369197, minimal case A001862.

The case of equality is A369198, covering case A368597.

A000085, A100861, A111924 count set partitions into singletons or pairs.

A006125 counts simple graphs, also loop-graphs if shifted left.

A006129 counts covering graphs, unlabeled A002494.

A054548 counts graphs covering n vertices with k edges, with loops A369199.

A322661 counts covering loop-graphs, unlabeled A322700.

A368927 counts choosable loop-graphs, covering A369140.

A369141 counts non-choosable loop-graphs, covering A369142.

Cf. A000169, A000272, A000666, A001187, A006649, A057500, A062740, A116508, A367863, A369145.

Programs

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n],{1,2}]],Length[#]<=Length[Union@@#]&]],{n,0,5}]

Formula

Binomial transform of A369194.