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A305844 Number of labeled spanning intersecting antichains on n vertices. 27
1, 1, 1, 5, 50, 2330, 1407712, 229800077244, 423295097236295093695 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 19 20:20 EDT 2019. Contains 326133 sequences. (Running on oeis4.)