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 A326364 Number of intersecting set systems with empty intersection (meaning there is no vertex in common to all the edges) covering n vertices. 4
 1, 0, 0, 2, 426, 987404, 887044205940, 291072121051815578010398, 14704019422368226413234332571239460300433492086, 12553242487939461785560846872353486129110194397301168776798213375239447299205732561174066488 (list; graph; refs; listen; history; text; internal format)
 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 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: A119120 A332142 A109931 * 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

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Last modified February 18 12:52 EST 2020. Contains 332018 sequences. (Running on oeis4.)