%I
%S 1,1,2,5,12,30,91,256,823,2656,9103
%N Number of nonisomorphic 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 nonisomorphic 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 Nonisomorphic 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 Nonisomorphic 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
