A319560 Number of non-isomorphic strict T_0 multiset partitions of weight n.

1, 1, 2, 6, 15, 40, 121, 353, 1107, 3550, 11818

Offset: 0

Author

Gus Wiseman, Sep 23 2018

Keywords

• nonn
• more

Comments

In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second. The T_0 condition means that there are no equivalent vertices.

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(4) = 15 multiset partitions:
1: {{1}}
2: {{1,1}}
   {{1},{2}}
3: {{1,1,1}}
   {{1,2,2}}
   {{1},{1,1}}
   {{1},{2,2}}
   {{2},{1,2}}
   {{1},{2},{3}}
4: {{1,1,1,1}}
   {{1,2,2,2}}
   {{1},{1,1,1}}
   {{1},{1,2,2}}
   {{1},{2,2,2}}
   {{1},{2,3,3}}
   {{2},{1,2,2}}
   {{1,1},{2,2}}
   {{1,2},{2,2}}
   {{1,3},{2,3}}
   {{1},{2},{1,2}}
   {{1},{2},{2,2}}
   {{1},{2},{3,3}}
   {{1},{3},{2,3}}
   {{1},{2},{3},{4}}
		

Crossrefs

Cf. A007716, A007718, A049311, A053419, A056156, A059201, A283877, A316980.

Cf. A319557, A319558, A319559, A319564, A319565, A319566, A319567.