A321484 Number of non-isomorphic self-dual connected multiset partitions of weight n.

1, 1, 1, 2, 3, 6, 9, 20, 35, 78, 141

Offset: 0

Author

Gus Wiseman, Nov 16 2018

Keywords

• nonn
• more

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.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(6) = 9 multiset partitions:
  {{1}}  {{11}}  {{111}}    {{1111}}    {{11111}}      {{111111}}
                 {{2}{12}}  {{12}{12}}  {{11}{122}}    {{112}{122}}
                            {{2}{122}}  {{12}{122}}    {{12}{1222}}
                                        {{2}{1222}}    {{2}{12222}}
                                        {{2}{13}{23}}  {{22}{1122}}
                                        {{3}{3}{123}}  {{12}{13}{23}}
                                                       {{2}{13}{233}}
                                                       {{3}{23}{123}}
                                                       {{3}{3}{1233}}
		

Crossrefs

Cf. A007718, A056156, A138178, A316983, A319565, A319616, A319647, A319719, A321194, A321585, A321680, A321681.