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 A318099 Number of non-isomorphic weight-n antichains of (not necessarily distinct) multisets whose dual is also an antichain of (not necessarily distinct) multisets. 32
 1, 1, 4, 7, 19, 32, 81, 142, 337, 659, 1564 (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 EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(3) = 7 antichains: 1: {{1}} 2: {{1,1}}    {{1,2}}    {{1},{1}}    {{1},{2}} 3: {{1,1,1}}    {{1,2,3}}    {{1},{2,2}}    {{1},{2,3}}    {{1},{1},{1}}    {{1},{2},{2}}    {{1},{2},{3}} CROSSREFS Cf. A000219, A006126, A007716, A049311, A059201, A283877, A306007, A316980, A316983, A319558, A319560, A319616-A319646, A300913. Sequence in context: A164265 A174465 A006381 * A274691 A102991 A298350 Adjacent sequences:  A318096 A318097 A318098 * A318100 A318101 A318102 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 25 2018 STATUS approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)