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 A326969 Number of sets of subsets of {1..n} whose dual is a weak antichain. 8
 2, 4, 12, 112, 38892 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The dual of a set of subsets 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}}. A weak antichain is a multiset of sets, none of which is a proper subset of any other. LINKS FORMULA a(n) = 2 * A326968(n). a(n) = 2 * Sum_{k = 0..n} binomial(n, k) * A326970(k). EXAMPLE The a(0) = 2 through a(2) = 12 sets of subsets:   {}    {}        {}   {{}}  {{}}      {{}}         {{1}}     {{1}}         {{},{1}}  {{2}}                   {{1,2}}                   {{},{1}}                   {{},{2}}                   {{1},{2}}                   {{},{1,2}}                   {{},{1},{2}}                   {{1},{2},{1,2}}                   {{},{1},{2},{1,2}} 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]]], stableQ[dual[#], SubsetQ]&]], {n, 0, 3}] CROSSREFS Sets of subsets whose dual is strict are A326941. The BII-numbers of set-systems whose dual is a weak antichain are A326966. Sets of subsets whose dual is a (strict) antichain are A326967. The case without empty edges is A326968. Cf. A001146, A059052, A326951, A326970, A326971, A326975, A326978. Sequence in context: A326950 A001696 A276534 * A304986 A013333 A154882 Adjacent sequences:  A326966 A326967 A326968 * A326970 A326971 A326972 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 10 2019 STATUS approved

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Last modified February 25 11:17 EST 2020. Contains 332234 sequences. (Running on oeis4.)