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 A319631 Number of non-isomorphic weight-n antichains of multisets whose dual is a chain of distinct multisets. 0
 1, 1, 2, 3, 5, 5, 13, 11, 25, 31, 54 (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(5) = 5 antichains: 1: {{1}} 2: {{1,1}}    {{1},{1}} 3: {{1,1,1}}    {{1,2,2}}    {{1},{1},{1}} 4: {{1,1,1,1}}    {{1,2,2,2}}    {{1,1},{1,1}}    {{1,2},{2,2}}    {{1},{1},{1},{1}} 5: {{1,1,1,1,1}}    {{1,1,2,2,2}}    {{1,2,2,2,2}}    {{1,2},{2,2,2}}    {{1},{1},{1},{1},{1}} CROSSREFS Cf. A000219, A006126, A007716, A059201, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913. Sequence in context: A156834 A079024 A342421 * A097453 A079125 A146305 Adjacent sequences:  A319628 A319629 A319630 * A319632 A319633 A319634 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 25 2018 STATUS approved

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Last modified September 20 18:29 EDT 2021. Contains 347588 sequences. (Running on oeis4.)