A319628 -id:A319628 - cp's OEIS frontend

A319641 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.

1, 1, 3, 5, 11, 18, 41, 70, 159, 323, 778

Offset: 0

Gus Wiseman, Sep 25 2018

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.

			Non-isomorphic representatives of the a(1) = 1 through a(4) = 11 antichains:
1: {{1}}
2: {{1,1}}
   {{1,2}}
   {{1},{2}}
3: {{1,1,1}}
   {{1,2,3}}
   {{1},{2,2}}
   {{1},{2,3}}
   {{1},{2},{3}}
4: {{1,1,1,1}}
   {{1,1,2,2}}
   {{1,2,3,4}}
   {{1},{2,2,2}}
   {{1},{2,3,4}}
   {{1,1},{2,2}}
   {{1,2},{3,3}}
   {{1,2},{3,4}}
   {{1},{2},{3,3}}
   {{1},{2},{3,4}}
   {{1},{2},{3},{4}}

Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646.

Euler transform of A319628.

cp's OEIS Frontend

A319641 Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.

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