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 A326366 Number of intersecting antichains of nonempty subsets of {1..n} with empty intersection (meaning there is no vertex in common to all the edges). 5
 1, 1, 1, 2, 28, 1960, 1379273, 229755337549, 423295079757497714059 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A set system (set of sets) is an antichain if no edge is a subset of any other, and is intersecting if no two edges are disjoint. LINKS FORMULA a(n) = A326375(n) - 1. a(n) = A001206(n+1) + A307249(n) - A014466(n). - Andrew Howroyd, Aug 14 2019 EXAMPLE The a(0) = 1 through a(4) = 28 intersecting antichains with empty intersection:   {}  {}  {}  {}              {}               {{12}{13}{23}}  {{12}{13}{23}}                               {{12}{14}{24}}                               {{13}{14}{34}}                               {{23}{24}{34}}                               {{12}{13}{234}}                               {{12}{14}{234}}                               {{12}{23}{134}}                               {{12}{24}{134}}                               {{13}{14}{234}}                               {{13}{23}{124}}                               {{13}{34}{124}}                               {{14}{24}{123}}                               {{14}{34}{123}}                               {{23}{24}{134}}                               {{23}{34}{124}}                               {{24}{34}{123}}                               {{12}{134}{234}}                               {{13}{124}{234}}                               {{14}{123}{234}}                               {{23}{124}{134}}                               {{24}{123}{134}}                               {{34}{123}{124}}                               {{12}{13}{14}{234}}                               {{12}{23}{24}{134}}                               {{13}{23}{34}{124}}                               {{14}{24}{34}{123}}                               {{123}{124}{134}{234}} 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}], Or[Intersection[#1, #2]=={}, SubsetQ[#1, #2]]&], #=={}||Intersection@@#=={}&]], {n, 0, 4}] CROSSREFS The case with empty edges allowed is A326375. Intersecting antichains of nonempty sets are A001206. Intersecting set systems with empty intersection are A326373. Antichains of nonempty sets with empty intersection are A006126 or A307249. The inverse binomial transform is the covering case A326365. Cf. A007363, A014466, A051185, A058891, A305001, A305843, A305844, A318128, A318129, A326361, A326362, A326363, A326364. Sequence in context: A063794 A238817 A202942 * A177400 A230700 A168554 Adjacent sequences:  A326363 A326364 A326365 * A326367 A326368 A326369 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 01 2019 EXTENSIONS a(7)-a(8) from Andrew Howroyd, Aug 14 2019 STATUS approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)