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 A326373 Number of intersecting set systems with empty intersection (meaning there is no vertex in common to all the edges) on n vertices. 3
 1, 1, 1, 3, 435, 989555, 887050136795, 291072121058024908202443, 14704019422368226413236661148207899662350666147, 12553242487939461785560846872353486129110194529637343578112251094358919036718815137721635299 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A set system (set of sets) is intersecting if no two edges are disjoint. LINKS FORMULA a(n) = A051185(n) - 1 - Sum_{k=1..n-1} binomial(n,k)*A000371(k). - Andrew Howroyd, Aug 12 2019 EXAMPLE The a(3) = 3 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[#=={}||Intersection@@#=={}]&]], {n, 0, 4}] CROSSREFS The inverse binomial transform is the covering case A326364. Set systems with empty intersection are A318129. Intersecting set systems are A051185. Intersecting antichains with empty intersection are A326366. Cf. A000371, A006126, A007363, A014466, A058891, A305844, A307249, A318128, A326361, A326362, A326363, A326365. Sequence in context: A277234 A269553 A086207 * A092052 A139999 A140870 Adjacent sequences:  A326370 A326371 A326372 * A326374 A326375 A326376 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 November 28 16:34 EST 2021. Contains 349413 sequences. (Running on oeis4.)