login
A319644
Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of distinct multisets.
1
1, 1, 2, 3, 5, 8, 18, 31, 73, 162, 413
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.
FORMULA
Euler transform of A319629.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(5) = 8 antichains:
1: {{1}}
2: {{1,1}}
{{1},{2}}
3: {{1,1,1}}
{{1},{2,2}}
{{1},{2},{3}}
4: {{1,1,1,1}}
{{1},{2,2,2}}
{{1,1},{2,2}}
{{1},{2},{3,3}}
{{1},{2},{3},{4}}
5: {{1,1,1,1,1}}
{{1},{2,2,2,2}}
{{1,1},{1,2,2}}
{{1,1},{2,2,2}}
{{1},{2},{3,3,3}}
{{1},{2,2},{3,3}}
{{1},{2},{3},{4,4}}
{{1},{2},{3},{4},{5}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 25 2018
STATUS
approved