A319782 Number of non-isomorphic intersecting strict T_0 multiset partitions of weight n.

1, 1, 1, 4, 7, 17, 42, 98, 248, 631, 1657

Offset: 0

Author

Gus Wiseman, Sep 27 2018

Keywords

• nonn
• more

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.

Examples

			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}}
		

Crossrefs

Cf. A007716, A049311, A059201, A281116, A283877, A305843, A305854, A306006, A316980.

Cf. A319755, A319759, A319760, A319765, A319779, A319787, A319789.