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 A319644 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of distinct multisets. 1
 1, 1, 2, 3, 5, 8, 18, 31, 73, 162, 413 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. LINKS FORMULA Euler transform of A319629. EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(5) = 8 antichains: 1: {{1}} 2: {{1,1}}    {{1},{2}} 3: {{1,1,1}}    {{1},{2,2}}    {{1},{2},{3}} 4: {{1,1,1,1}}    {{1},{2,2,2}}    {{1,1},{2,2}}    {{1},{2},{3,3}}    {{1},{2},{3},{4}} 5: {{1,1,1,1,1}}    {{1},{2,2,2,2}}    {{1,1},{1,2,2}}    {{1,1},{2,2,2}}    {{1},{2},{3,3,3}}    {{1},{2,2},{3,3}}    {{1},{2},{3},{4,4}}    {{1},{2},{3},{4},{5}} CROSSREFS Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646. Sequence in context: A113879 A205303 A025071 * A049908 A135568 A103004 Adjacent sequences:  A319641 A319642 A319643 * A319645 A319646 A319647 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 25 2018 STATUS approved

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Last modified July 20 16:24 EDT 2019. Contains 325185 sequences. (Running on oeis4.)