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A319618
Number of non-isomorphic weight-n antichains of multisets whose dual is a chain of multisets.
0
1, 1, 3, 4, 9, 10, 24, 28, 57, 80, 138
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.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 9 antichains:
1: {{1}}
2: {{1,1}}
{{1,2}}
{{1},{1}}
3: {{1,1,1}}
{{1,2,2}}
{{1,2,3}}
{{1},{1},{1}}
4: {{1,1,1,1}}
{{1,1,2,2}}
{{1,2,2,2}}
{{1,2,3,3}}
{{1,2,3,4}}
{{1,1},{1,1}}
{{1,2},{1,2}}
{{1,2},{2,2}}
{{1},{1},{1},{1}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 25 2018
STATUS
approved