OFFSET
0,4
COMMENTS
Also the number of (0,1) 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.
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(1) = 1 through a(8) = 16 set systems:
{{1}} {{1}{2}} {{2}{12}} {{1}{3}{23}} {{2}{13}{23}}
{{1}{2}{3}} {{1}{2}{3}{4}} {{1}{2}{4}{34}}
{{1}{2}{3}{4}{5}}
.
{{12}{13}{23}} {{13}{23}{123}} {{1}{13}{14}{234}}
{{3}{23}{123}} {{1}{23}{24}{34}} {{12}{13}{24}{34}}
{{1}{3}{24}{34}} {{1}{4}{34}{234}} {{1}{24}{34}{234}}
{{2}{4}{12}{34}} {{2}{13}{24}{34}} {{2}{14}{34}{234}}
{{1}{2}{3}{5}{45}} {{3}{4}{14}{234}} {{3}{4}{134}{234}}
{{1}{2}{3}{4}{5}{6}} {{1}{2}{4}{35}{45}} {{4}{13}{14}{234}}
{{1}{3}{5}{23}{45}} {{1}{2}{34}{35}{45}}
{{1}{2}{3}{4}{6}{56}} {{1}{2}{5}{45}{345}}
{{1}{2}{3}{4}{5}{6}{7}} {{1}{3}{24}{35}{45}}
{{1}{4}{5}{25}{345}}
{{2}{4}{12}{35}{45}}
{{4}{5}{13}{23}{45}}
{{1}{2}{3}{5}{46}{56}}
{{1}{2}{4}{6}{34}{56}}
{{1}{2}{3}{4}{5}{7}{67}}
{{1}{2}{3}{4}{5}{6}{7}{8}}
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 15 2018
STATUS
approved