cp's OEIS Frontend

A319628 Number of non-isomorphic connected weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.

%I A319628 #6 Sep 25 2018 20:46:26
%S A319628 1,1,2,2,3,3,10,11,37,80,233
%N A319628 Number of non-isomorphic connected weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.
%C A319628 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 A319628 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 A319628 Euler transform is A319641.
%e A319628 Non-isomorphic representatives of the a(1) = 1 through a(6) = 10 antichains:
%e A319628 1: {{1}}
%e A319628 2: {{1,1}}
%e A319628    {{1,2}}
%e A319628 3: {{1,1,1}}
%e A319628    {{1,2,3}}
%e A319628 4: {{1,1,1,1}}
%e A319628    {{1,1,2,2}}
%e A319628    {{1,2,3,4}}
%e A319628 5: {{1,1,1,1,1}}
%e A319628    {{1,2,3,4,5}}
%e A319628    {{1,1},{1,2,2}}
%e A319628 6: {{1,1,1,1,1,1}}
%e A319628    {{1,1,1,2,2,2}}
%e A319628    {{1,1,2,2,3,3}}
%e A319628    {{1,2,3,4,5,6}}
%e A319628    {{1,1},{1,2,2,2}}
%e A319628    {{1,1,2},{1,2,2}}
%e A319628    {{1,1,2},{2,2,2}}
%e A319628    {{1,1,2},{2,3,3}}
%e A319628    {{1,1},{1,2},{2,2}}
%e A319628    {{1,2},{1,3},{2,3}}
%Y A319628 Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319558, A319565, A319616-A319646.
%K A319628 nonn,more
%O A319628 0,3
%A A319628 _Gus Wiseman_, Sep 25 2018