A319625 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of distinct sets.

1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 3

Offset

0,11

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

Table of n, a(n) for n=0..10.

Formula

Euler transform is A319638.

Example

Non-isomorphic representatives of the a(1) = 1 through a(10) = 3 antichains:
               {{1}}
        {{1,2},{1,3},{2,3}}
     {{1,2},{1,3},{2,4},{3,4}}
    {{1,2},{1,3},{1,4},{2,3,4}}
   {{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, A319558, A319565, A319616-A319646.

Sequence in context: A065803 A160540 A186718 * A307802 A169585 A045840

Adjacent sequences: A319622 A319623 A319624 * A319626 A319627 A319628

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved