login
A319782
Number of non-isomorphic intersecting strict T_0 multiset partitions of weight n.
4
1, 1, 1, 4, 7, 17, 42, 98, 248, 631, 1657
OFFSET
0,4
COMMENTS
A multiset partition is intersecting iff no two parts are disjoint. The weight of a multiset partition is the sum of sizes of its parts. 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 T_0 condition means the dual is strict.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 multiset partitions:
1: {{1}}
2: {{1,1}}
3: {{1,1,1}}
{{1,2,2}}
{{1},{1,1}}
{{2},{1,2}}
4: {{1,1,1,1}}
{{1,2,2,2}}
{{1},{1,1,1}}
{{1},{1,2,2}}
{{2},{1,2,2}}
{{1,2},{2,2}}
{{1,3},{2,3}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 27 2018
STATUS
approved