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Number of non-isomorphic weight-n antichains (not necessarily strict) of sets.
9

%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