A326364 Number of intersecting set systems with empty intersection (meaning there is no vertex in common to all the edges) covering n vertices.

1, 0, 0, 2, 426, 987404, 887044205940, 291072121051815578010398, 14704019422368226413234332571239460300433492086, 12553242487939461785560846872353486129110194397301168776798213375239447299205732561174066488

Offset

0,4

Comments

Covering means there are no isolated vertices. A set system (set of sets) is intersecting if no two edges are disjoint.

Links

Table of n, a(n) for n=0..9.

Formula

Inverse binomial transform of A326373. - Andrew Howroyd, Aug 12 2019

Example

The a(3) = 2 intersecting set systems with empty intersection:
  {{1,2},{1,3},{2,3}}
  {{1,2},{1,3},{2,3},{1,2,3}}

Mathematica

stableSets[u_, Q_]:=If[Length[u]==0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r==w||Q[r, w]||Q[w, r]], Q]]]];
Table[Length[Select[stableSets[Subsets[Range[n], {1, n}], Intersection[#1, #2]=={}&], And[Union@@#==Range[n], #=={}||Intersection@@#=={}]&]], {n, 0, 4}]

Crossrefs

Covering set systems with empty intersection are A318128.

Covering, intersecting set systems are A305843.

Covering, intersecting antichains with empty intersection are A326365.

Cf. A006126, A007363, A014466, A051185, A058891, A305844, A307249, A318129, A326361, A326362, A326363.

Sequence in context: A332142 A109931 A352498 * A200951 A118710 A159513

Adjacent sequences: A326361 A326362 A326363 * A326365 A326366 A326367

Keyword

nonn

Author

Gus Wiseman, Jul 01 2019

Extensions

a(6)-a(9) from Andrew Howroyd, Aug 12 2019

Status

approved