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 A319622 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of (not necessarily distinct) sets. 0
 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 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(10) = 7 antichains: 1:  {{1}} 2:  {{1,2}} 3:  {{1,2,3}} 4:  {{1,2,3,4}} 5:  {{1,2,3,4,5}} 6:  {{1,2,3,4,5,6}}     {{1,2},{1,3},{2,3}} 7:  {{1,2,3,4,5,6,7}} 8:  {{1,2,3,4,5,6,7,8}}     {{1,2},{1,3,4},{2,3,4}}     {{1,2},{1,3},{2,4},{3,4}} 9:  {{1,2,3,4,5,6,7,8,9}}     {{1,2},{1,3},{1,4},{2,3,4}} 10: {{1,2,3,4,5,6,7,8,9,10}}     {{1,2},{1,3,4,5},{2,3,4,5}}     {{1,2,3},{1,4,5},{2,3,4,5}}     {{1,2},{1,3},{2,4,5},{3,4,5}}     {{1,3},{2,4},{1,2,5},{3,4,5}}     {{1,2},{1,3},{2,4},{3,5},{4,5}}     {{1,3},{1,4},{2,3},{2,4},{3,4}} CROSSREFS Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913. Sequence in context: A022477 A238944 A144238 * A082833 A101709 A005247 Adjacent sequences:  A319619 A319620 A319621 * A319623 A319624 A319625 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 25 2018 STATUS approved

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Last modified April 18 22:02 EDT 2021. Contains 343090 sequences. (Running on oeis4.)