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Number of non-isomorphic connected strict T_0 multiset partitions of weight n.
20

%I #10 Sep 24 2018 08:58:09

%S 1,1,1,4,8,21,62,175,553,1775,6007

%N Number of non-isomorphic connected strict T_0 multiset partitions of weight n.

%C In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second. The T_0 condition means that there are no equivalent vertices.

%C The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

%e Non-isomorphic representatives of the a(1) = 1 through a(4) = 8 multiset partitions:

%e 1: {{1}}

%e 2: {{1,1}}

%e 3: {{1,1,1}}

%e {{1,2,2}}

%e {{1},{1,1}}

%e {{2},{1,2}}

%e 4: {{1,1,1,1}}

%e {{1,2,2,2}}

%e {{1},{1,1,1}}

%e {{1},{1,2,2}}

%e {{2},{1,2,2}}

%e {{1,2},{2,2}}

%e {{1,3},{2,3}}

%e {{1},{2},{1,2}}

%Y Cf. A007716, A007718, A049311, A056156, A059201, A283877, A316980.

%Y Cf. A319557, A319558, A319559, A319560, A319564, A319566, A319567.

%K nonn,more

%O 0,4

%A _Gus Wiseman_, Sep 23 2018