cp's OEIS Frontend

A319629 Number of non-isomorphic connected weight-n antichains of distinct multisets whose dual is also an antichain of distinct multisets.

%I A319629 #6 Sep 25 2018 20:46:37
%S A319629 1,1,1,1,1,2,7,9,29,66,189
%N A319629 Number of non-isomorphic connected weight-n antichains of distinct multisets whose dual is also an antichain of distinct multisets.
%C A319629 The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.
%C A319629 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%F A319629 Euler transform is A319644.
%e A319629 Non-isomorphic representatives of the a(1) = 1 through a(7) = 9 antichains:
%e A319629 1: {{1}}
%e A319629 2: {{1,1}}
%e A319629 3: {{1,1,1}}
%e A319629 4: {{1,1,1,1}}
%e A319629 5: {{1,1,1,1,1}}
%e A319629    {{1,1},{1,2,2}}
%e A319629 6: {{1,1,1,1,1,1}}
%e A319629    {{1,1},{1,2,2,2}}
%e A319629    {{1,1,2},{1,2,2}}
%e A319629    {{1,1,2},{2,2,2}}
%e A319629    {{1,1,2},{2,3,3}}
%e A319629    {{1,1},{1,2},{2,2}}
%e A319629    {{1,2},{1,3},{2,3}}
%e A319629 7: {{1,1,1,1,1,1,1}}
%e A319629    {{1,1},{1,2,2,2,2}}
%e A319629    {{1,1,1},{1,2,2,2}}
%e A319629    {{1,1,2},{1,2,2,2}}
%e A319629    {{1,1,2},{2,2,2,2}}
%e A319629    {{1,1,2},{2,3,3,3}}
%e A319629    {{1,1},{1,2},{2,2,2}}
%e A319629    {{1,1},{1,2},{2,3,3}}
%e A319629    {{1,2},{1,3},{2,3,3}}
%Y A319629 Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319558, A319565, A319616-A319646.
%K A319629 nonn,more
%O A319629 0,6
%A A319629 _Gus Wiseman_, Sep 25 2018