OFFSET
0,5
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 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
Non-isomorphic representatives of the a(2) = 1 through a(7) = 14 multiset partitions:
{{11}} {{111}} {{1111}} {{11111}} {{111111}} {{1111111}}
{{11}{22}} {{11}{122}} {{111}{222}} {{111}{1222}}
{{11}{222}} {{112}{122}} {{111}{2222}}
{{12}{122}} {{11}{2222}} {{112}{1222}}
{{12}{1222}} {{11}{22222}}
{{22}{1122}} {{12}{12222}}
{{11}{22}{33}} {{122}{1122}}
{{12}{13}{23}} {{22}{11222}}
{{11}{12}{233}}
{{11}{22}{233}}
{{11}{22}{333}}
{{11}{23}{233}}
{{12}{13}{233}}
{{13}{23}{123}}
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 09 2018
STATUS
approved