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%I #4 Nov 18 2018 15:06:21
%S 1,1,3,5,12,19,45,75,170,314,713
%N Number of non-isomorphic weight-n antichains (not necessarily strict) of sets.
%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(5) = 19 antichains:
%e {{1}} {{1,2}} {{1,2,3}} {{1,2,3,4}} {{1,2,3,4,5}}
%e {{1},{1}} {{1},{2,3}} {{1,2},{1,2}} {{1},{2,3,4,5}}
%e {{1},{2}} {{1},{1},{1}} {{1},{2,3,4}} {{1,2},{3,4,5}}
%e {{1},{2},{2}} {{1,2},{3,4}} {{1,4},{2,3,4}}
%e {{1},{2},{3}} {{1,3},{2,3}} {{1},{1},{2,3,4}}
%e {{1},{1},{2,3}} {{1},{2,3},{2,3}}
%e {{1},{2},{3,4}} {{1},{2},{3,4,5}}
%e {{1},{1},{1},{1}} {{1},{2,3},{4,5}}
%e {{1},{1},{2},{2}} {{1},{2,4},{3,4}}
%e {{1},{2},{2},{2}} {{1},{1},{1},{2,3}}
%e {{1},{2},{3},{3}} {{1},{2},{2},{3,4}}
%e {{1},{2},{3},{4}} {{1},{2},{3},{4,5}}
%e {{1},{1},{1},{1},{1}}
%e {{1},{1},{2},{2},{2}}
%e {{1},{2},{2},{2},{2}}
%e {{1},{2},{2},{3},{3}}
%e {{1},{2},{3},{3},{3}}
%e {{1},{2},{3},{4},{4}}
%e {{1},{2},{3},{4},{5}}
%Y Cf. A006126, A049311, A096827, A285572, A293993, A293994, A318099, A319719, A319721, A320799, A321678.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Nov 16 2018
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