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%I #4 Nov 27 2018 16:18:20
%S 1,1,1,1,2,2,3,5,10,18,30
%N Number of non-isomorphic self-dual connected antichains of multisets 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}}. A multiset partition is self-dual if it is isomorphic to its dual. For example, {{1,1},{1,2,2},{2,3,3}} is self-dual, as it is isomorphic to its dual {{1,1,2},{2,2,3},{3,3}}.
%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(9) = 18 antichains:
%e {{1}} {{11}} {{111}} {{1111}} {{11111}} {{111111}}
%e {{12}{12}} {{11}{122}} {{112}{122}}
%e {{12}{13}{23}}
%e .
%e {{1111111}} {{11111111}} {{111111111}}
%e {{111}{1222}} {{111}{11222}} {{1111}{12222}}
%e {{112}{1222}} {{1112}{1222}} {{1112}{11222}}
%e {{11}{12}{233}} {{112}{12222}} {{1112}{12222}}
%e {{12}{13}{233}} {{1122}{1122}} {{112}{122222}}
%e {{11}{122}{233}} {{11}{11}{12233}}
%e {{12}{13}{2333}} {{11}{122}{1233}}
%e {{13}{112}{233}} {{112}{123}{233}}
%e {{13}{122}{233}} {{113}{122}{233}}
%e {{12}{13}{24}{34}} {{12}{111}{2333}}
%e {{12}{13}{23333}}
%e {{12}{133}{2233}}
%e {{123}{123}{123}}
%e {{13}{112}{2333}}
%e {{22}{113}{2333}}
%e {{12}{13}{14}{234}}
%e {{12}{13}{22}{344}}
%e {{12}{13}{24}{344}}
%Y Cf. A006126, A007716, A007718, A286520, A293993, A293994, A304867, A316983, A318099, A319719, A319721, A322111, A322112.
%K nonn,more
%O 0,5
%A _Gus Wiseman_, Nov 26 2018
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