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 A319619 Number of non-isomorphic connected weight-n antichains of multisets whose dual is also an antichain of multisets. 0
 1, 1, 3, 3, 6, 4, 15, 13, 48, 96, 280 (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 is A318099. EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(5) = 4 antichains: 1: {{1}} 2: {{1,1}}    {{1,2}}    {{1},{1}} 3: {{1,1,1}}    {{1,2,3}}    {{1},{1},{1}} 4: {{1,1,1,1}}    {{1,1,2,2}}    {{1,2,3,4}}    {{1,1},{1,1}}    {{1,2},{1,2}}    {{1},{1},{1},{1}} 5: {{1,1,1,1,1}}    {{1,2,3,4,5}}    {{1,1},{1,2,2}}    {{1},{1},{1},{1},{1}} CROSSREFS Cf. A006126, A007716, A007718, A056156, A059201, A316980, A316983, A318099, A319557, A319558, A319565, A319616-A319646, A300913. Sequence in context: A137462 A163926 A050346 * A309001 A142149 A132119 Adjacent sequences:  A319616 A319617 A319618 * A319620 A319621 A319622 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 25 2018 STATUS approved

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Last modified April 19 00:03 EDT 2021. Contains 343098 sequences. (Running on oeis4.)