cp's OEIS Frontend

A319622 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of (not necessarily distinct) sets.

%I A319622 #7 Oct 26 2018 12:50:18
%S A319622 1,1,1,1,1,1,2,1,3,2,7
%N A319622 Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of (not necessarily distinct) sets.
%C A319622 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 A319622 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 A319622 Non-isomorphic representatives of the a(1) = 1 through a(10) = 7 antichains:
%e A319622 1:  {{1}}
%e A319622 2:  {{1,2}}
%e A319622 3:  {{1,2,3}}
%e A319622 4:  {{1,2,3,4}}
%e A319622 5:  {{1,2,3,4,5}}
%e A319622 6:  {{1,2,3,4,5,6}}
%e A319622     {{1,2},{1,3},{2,3}}
%e A319622 7:  {{1,2,3,4,5,6,7}}
%e A319622 8:  {{1,2,3,4,5,6,7,8}}
%e A319622     {{1,2},{1,3,4},{2,3,4}}
%e A319622     {{1,2},{1,3},{2,4},{3,4}}
%e A319622 9:  {{1,2,3,4,5,6,7,8,9}}
%e A319622     {{1,2},{1,3},{1,4},{2,3,4}}
%e A319622 10: {{1,2,3,4,5,6,7,8,9,10}}
%e A319622     {{1,2},{1,3,4,5},{2,3,4,5}}
%e A319622     {{1,2,3},{1,4,5},{2,3,4,5}}
%e A319622     {{1,2},{1,3},{2,4,5},{3,4,5}}
%e A319622     {{1,3},{2,4},{1,2,5},{3,4,5}}
%e A319622     {{1,2},{1,3},{2,4},{3,5},{4,5}}
%e A319622     {{1,3},{1,4},{2,3},{2,4},{3,4}}
%Y A319622 Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913.
%K A319622 nonn,more
%O A319622 0,7
%A A319622 _Gus Wiseman_, Sep 25 2018