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 A326950 Number of T_0 antichains of nonempty subsets of {1..n}. 7
 1, 2, 4, 12, 107, 6439, 7726965, 2414519001532, 56130437161079183223017 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges). LINKS FORMULA Binomial transform of A245567, if we assume A245567(0) = 1. EXAMPLE The a(0) = 1 through a(3) = 12 antichains:   {}  {}     {}         {}       {{1}}  {{1}}      {{1}}              {{2}}      {{2}}              {{1},{2}}  {{3}}                         {{1},{2}}                         {{1},{3}}                         {{2},{3}}                         {{1,2},{1,3}}                         {{1,2},{2,3}}                         {{1},{2},{3}}                         {{1,3},{2,3}}                         {{1,2},{1,3},{2,3}} MATHEMATICA dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}]; stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}]; Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], stableQ[#, SubsetQ]&&UnsameQ@@dual[#]&]], {n, 0, 3}] CROSSREFS Antichains of nonempty sets are A014466. T_0 set-systems are A326940. The covering case is A245567. Cf. A006126, A059201, A059052, A245567, A319559, A319564, A326030, A326946, A326947. Sequence in context: A325502 A038791 A327563 * A001696 A276534 A326969 Adjacent sequences:  A326947 A326948 A326949 * A326951 A326952 A326953 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 08 2019 EXTENSIONS a(5)-a(8) from Andrew Howroyd, Aug 14 2019 STATUS approved

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Last modified October 15 05:43 EDT 2019. Contains 328026 sequences. (Running on oeis4.)