A327070 Number of non-connected simple labeled graphs covering n vertices.

1, 0, 0, 0, 3, 40, 745, 21028, 973889, 80133088, 12523299729, 3847333778244, 2341705361100633, 2821794389863015840, 6728707109106848947081, 31769173063866390661714996, 297278309767391164611330317921

Offset: 0

Author

Gus Wiseman, Aug 24 2019

Keywords

• nonn

Comments

We consider the empty graph to be neither connected (one component) nor disconnected (more than one component).

Examples

			The a(4) = 3 graphs:
  {{1,2},{3,4}}
  {{1,3},{2,4}}
  {{1,4},{2,3}}
		

Crossrefs

Column k = 0 of A327149.

The unlabeled version is A327075.

The non-covering version is A327199.

Cf. A000719, A001187, A001349, A002494, A006125, A006129, A054592, A327070.

Programs

Mathematica

csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Union@@#==Range[n]&&Length[csm[#]]!=1&]],{n,0,5}]

Formula

a(n) = A006129(n) - A001187(n), if we assume A001187(0) = 0 and A001187(1) = 0.

Inverse binomial transform of A327199.