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%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
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