A305844 Number of labeled spanning intersecting antichains on n vertices.

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

Offset

0,4

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.

Links

Table of n, a(n) for n=0..8.

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

Formula

Inverse binomial transform of A001206(n + 1).

Example

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}}

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}]

Crossrefs

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

Sequence in context: A082100 A299353 A180976 * A303132 A070995 A063803

Adjacent sequences: A305841 A305842 A305843 * A305845 A305846 A305847

Keyword

nonn

Author

Gus Wiseman, Jun 11 2018

Status

approved