OFFSET
0,3
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}}.
EXAMPLE
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
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 09 2018
STATUS
approved