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 A319557 Number of non-isomorphic strict connected multiset partitions of weight n. 25

%I

%S 1,1,2,5,12,30,91,256,823,2656,9103

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

%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.

%C Also the number of non-isomorphic connected T_0 multiset partitions of weight n. 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.

%F Inverse Euler transform of A316980.

%e Non-isomorphic representatives of the a(4) = 12 strict connected multiset partitions:

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

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

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

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

%e {{1,2,3,4}}

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

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

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

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

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

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

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

%e Non-isomorphic representatives of the a(4) = 12 connected T_0 multiset partitions:

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

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

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

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

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

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

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

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

%Y Cf. A319558, A319559, A319560, A319564, A319565, A319566, A319567.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Sep 23 2018

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Last modified June 19 03:38 EDT 2021. Contains 345125 sequences. (Running on oeis4.)