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A321739
Number of non-isomorphic weight-n set multipartitions (multisets of sets) whose part-sizes are also their vertex-degrees.
5
1, 1, 1, 2, 4, 6, 12, 21, 46, 94, 208
OFFSET
0,4
COMMENTS
Also the number of (0,1) square matrices up to row and column permutations with n ones and no zero rows or columns, with the same multiset of row sums as of column sums.
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(6) = 12 set multipartitions:
{1} {1}{2} {2}{12} {12}{12} {1}{23}{23} {12}{13}{23}
{1}{2}{3} {1}{1}{23} {2}{13}{23} {3}{23}{123}
{1}{3}{23} {3}{3}{123} {1}{1}{1}{234}
{1}{2}{3}{4} {1}{2}{2}{34} {1}{1}{24}{34}
{1}{2}{4}{34} {1}{2}{34}{34}
{1}{2}{3}{4}{5} {1}{3}{24}{34}
{1}{4}{4}{234}
{2}{4}{12}{34}
{3}{4}{12}{34}
{1}{2}{3}{3}{45}
{1}{2}{3}{5}{45}
{1}{2}{3}{4}{5}{6}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 19 2018
STATUS
approved