A319619 Number of non-isomorphic connected weight-n antichains of multisets whose dual is also an antichain of multisets.

1, 1, 3, 3, 6, 4, 15, 13, 48, 96, 280

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

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

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: A163926 A362334 A050346 * A309001 A142149 A132119

Adjacent sequences: A319616 A319617 A319618 * A319620 A319621 A319622

Keyword

nonn,more

Author

Gus Wiseman, Sep 25 2018

Status

approved