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%I #5 Nov 18 2018 15:06:28
%S 1,1,3,4,9,14,39,80,216,538,1460
%N Number of non-isomorphic weight-n connected antichains (not necessarily strict) of multisets with multiset density -1.
%C The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.
%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) = 14 multiset trees:
%e {{1}} {{1,1}} {{1,1,1}} {{1,1,1,1}} {{1,1,1,1,1}}
%e {{1,2}} {{1,2,2}} {{1,1,2,2}} {{1,1,2,2,2}}
%e {{1},{1}} {{1,2,3}} {{1,2,2,2}} {{1,2,2,2,2}}
%e {{1},{1},{1}} {{1,2,3,3}} {{1,2,2,3,3}}
%e {{1,2,3,4}} {{1,2,3,3,3}}
%e {{1,1},{1,1}} {{1,2,3,4,4}}
%e {{1,2},{2,2}} {{1,2,3,4,5}}
%e {{1,3},{2,3}} {{1,1},{1,2,2}}
%e {{1},{1},{1},{1}} {{1,2},{2,2,2}}
%e {{1,2},{2,3,3}}
%e {{1,3},{2,3,3}}
%e {{1,4},{2,3,4}}
%e {{3,3},{1,2,3}}
%e {{1},{1},{1},{1},{1}}
%Y Cf. A006126, A007718, A056156, A096827, A285572, A293993, A293994, A305052, A319719, A319721, A321194, A321585, A321681.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Nov 16 2018