
COMMENTS

Also the number of 01 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 are all different and none sums to 1.
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.


EXAMPLE

Nonisomorphic representatives of the a(6) = 1 through a(10) = 4 set systems:
6: {{1,2},{1,3},{2,3}}
7: {{1,3},{2,3},{1,2,3}}
8: {{1,2},{1,3},{2,4},{3,4}}
9: {{1,2},{1,3},{1,4},{2,3,4}}
9: {{1,2},{1,4},{3,4},{2,3,4}}
10: {{1,2},{2,4},{1,3,4},{2,3,4}}
10: {{1,3},{2,4},{1,3,4},{2,3,4}}
10: {{1,4},{2,4},{3,4},{1,2,3,4}}
10: {{1,2},{1,3},{2,4},{3,5},{4,5}}
