A321401 Number of non-isomorphic strict self-dual multiset partitions of weight n.

1, 1, 2, 4, 7, 14, 29, 57, 117, 240, 498

Offset: 0

Author

Gus Wiseman, Nov 09 2018

Keywords

• nonn
• more

Comments

Also the number of nonnegative integer symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which the rows (or columns) are all different.

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}}.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(5) = 14 multiset partitions:
  {{1}}  {{1,1}}    {{1,1,1}}      {{1,1,1,1}}        {{1,1,1,1,1}}
         {{1},{2}}  {{1},{2,2}}    {{1,1},{2,2}}      {{1,1},{1,2,2}}
                    {{2},{1,2}}    {{1},{2,2,2}}      {{1,1},{2,2,2}}
                    {{1},{2},{3}}  {{2},{1,2,2}}      {{1,2},{1,2,2}}
                                   {{1},{2},{3,3}}    {{1},{2,2,2,2}}
                                   {{1},{3},{2,3}}    {{2},{1,2,2,2}}
                                   {{1},{2},{3},{4}}  {{1},{2,2},{3,3}}
                                                      {{1},{2},{3,3,3}}
                                                      {{1},{3},{2,3,3}}
                                                      {{2},{1,2},{3,3}}
                                                      {{2},{1,3},{2,3}}
                                                      {{1},{2},{3},{4,4}}
                                                      {{1},{2},{4},{3,4}}
                                                      {{1},{2},{3},{4},{5}}
		

Crossrefs

Cf. A000219, A007716, A045778, A059201, A316980, A316983, A319560, A319616.

Cf. A320796, A320797, A321402, A321405, A321406, A321407.