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A319629
Number of non-isomorphic connected weight-n antichains of distinct multisets whose dual is also an antichain of distinct multisets.
4
1, 1, 1, 1, 1, 2, 7, 9, 29, 66, 189
OFFSET
0,6
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 is A319644.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(7) = 9 antichains:
1: {{1}}
2: {{1,1}}
3: {{1,1,1}}
4: {{1,1,1,1}}
5: {{1,1,1,1,1}}
{{1,1},{1,2,2}}
6: {{1,1,1,1,1,1}}
{{1,1},{1,2,2,2}}
{{1,1,2},{1,2,2}}
{{1,1,2},{2,2,2}}
{{1,1,2},{2,3,3}}
{{1,1},{1,2},{2,2}}
{{1,2},{1,3},{2,3}}
7: {{1,1,1,1,1,1,1}}
{{1,1},{1,2,2,2,2}}
{{1,1,1},{1,2,2,2}}
{{1,1,2},{1,2,2,2}}
{{1,1,2},{2,2,2,2}}
{{1,1,2},{2,3,3,3}}
{{1,1},{1,2},{2,2,2}}
{{1,1},{1,2},{2,3,3}}
{{1,2},{1,3},{2,3,3}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 25 2018
STATUS
approved