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A320799
Number of non-isomorphic (not necessarily strict) antichains of multisets of weight n with no singletons or leaves (vertices that appear only once).
4
1, 0, 1, 1, 5, 4, 22, 27, 107, 212, 689
OFFSET
0,5
COMMENTS
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) = 27 multiset partitions:
{{11}} {{111}} {{1111}} {{11111}} {{111111}} {{1111111}}
{{1122}} {{11222}} {{111222}} {{1112222}}
{{11}{11}} {{11}{122}} {{112222}} {{1122222}}
{{11}{22}} {{11}{222}} {{112233}} {{1122333}}
{{12}{12}} {{111}{111}} {{111}{1222}}
{{11}{1222}} {{11}{12222}}
{{111}{222}} {{111}{2222}}
{{112}{122}} {{11}{12233}}
{{11}{2222}} {{111}{2233}}
{{112}{222}} {{112}{1222}}
{{11}{2233}} {{11}{22222}}
{{112}{233}} {{112}{2222}}
{{122}{122}} {{11}{22333}}
{{123}{123}} {{112}{2333}}
{{11}{11}{11}} {{113}{2233}}
{{11}{12}{22}} {{122}{1233}}
{{11}{22}{22}} {{222}{1122}}
{{11}{22}{33}} {{11}{11}{122}}
{{11}{23}{23}} {{11}{11}{222}}
{{12}{12}{12}} {{11}{12}{222}}
{{12}{12}{22}} {{11}{12}{233}}
{{12}{13}{23}} {{11}{22}{233}}
{{11}{22}{333}}
{{12}{12}{222}}
{{12}{12}{233}}
{{12}{12}{333}}
{{12}{13}{233}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 02 2018
STATUS
approved