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A319768
Number of non-isomorphic strict multiset partitions (sets of multisets) of weight n whose dual is a (not necessarily strict) intersecting multiset partition.
6
1, 1, 2, 5, 11, 25, 63, 144, 364, 905, 2356
OFFSET
0,3
COMMENTS
The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts 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.
A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 11 multiset partitions:
1: {{1}}
2: {{1,1}}
{{1,2}}
3: {{1,1,1}}
{{1,2,2}}
{{1,2,3}}
{{1},{1,1}}
{{2},{1,2}}
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},{1,2,2}}
{{2},{1,2,2}}
{{3},{1,2,3}}
{{1,2},{2,2}}
{{1},{2},{1,2}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 27 2018
STATUS
approved