A305844 Number of labeled spanning intersecting antichains on n vertices.

1, 1, 1, 5, 50, 2330, 1407712, 229800077244, 423295097236295093695

Offset: 0

Author

Gus Wiseman, Jun 11 2018

Keywords

• nonn

Comments

An intersecting antichain S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection, and none of which is a subset of any other. S is spanning if every vertex is contained in some edge.

Examples

			The a(3) = 5 spanning intersecting antichains:
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,3},{2,3}}
		

Links

• Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Crossrefs

Cf. A001206, A006126, A048143, A051185, A134958, A030019, A304985, A305843.

Programs

Mathematica

Length/@Table[Select[Subsets[Rest[Subsets[Range[n]]]],And[Union@@#==Range[n],FreeQ[Intersection@@@Tuples[#,2],{},{1}],Select[Tuples[#,2],UnsameQ@@#&&Complement@@#=={}&]=={}]&],{n,1,4}]

Formula

Inverse binomial transform of A001206(n + 1).