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%I #20 Nov 18 2018 15:05:58
%S 1,1,1,2,3,6,9,20,35,78,141
%N Number of non-isomorphic self-dual connected multiset partitions of weight n.
%C The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.
%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(6) = 9 multiset partitions:
%e {{1}} {{11}} {{111}} {{1111}} {{11111}} {{111111}}
%e {{2}{12}} {{12}{12}} {{11}{122}} {{112}{122}}
%e {{2}{122}} {{12}{122}} {{12}{1222}}
%e {{2}{1222}} {{2}{12222}}
%e {{2}{13}{23}} {{22}{1122}}
%e {{3}{3}{123}} {{12}{13}{23}}
%e {{2}{13}{233}}
%e {{3}{23}{123}}
%e {{3}{3}{1233}}
%Y Cf. A007718, A056156, A138178, A316983, A319565, A319616, A319647, A319719, A321194, A321585, A321680, A321681.
%K nonn,more
%O 0,4
%A _Gus Wiseman_, Nov 16 2018
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