cp's OEIS Frontend

A326971 Number of unlabeled set-systems on n vertices whose dual is a weak antichain.

%I A326971 #7 Aug 12 2019 22:32:24
%S A326971 1,2,5,24,1267
%N A326971 Number of unlabeled set-systems on n vertices whose dual is a weak antichain.
%C A326971 A set-system is a finite set of finite nonempty sets. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. A weak antichain is a multiset of sets, none of which is a proper subset of any other.
%e A326971 Non-isomorphic representatives of the a(0) = 1 through a(3) = 24 set-systems:
%e A326971   {}  {}     {}               {}
%e A326971       {{1}}  {{1}}            {{1}}
%e A326971              {{1,2}}          {{1,2}}
%e A326971              {{1},{2}}        {{1},{2}}
%e A326971              {{1},{2},{1,2}}  {{1,2,3}}
%e A326971                               {{1},{2,3}}
%e A326971                               {{1},{2},{3}}
%e A326971                               {{1},{2},{1,2}}
%e A326971                               {{1,2},{1,3},{2,3}}
%e A326971                               {{1},{2,3},{1,2,3}}
%e A326971                               {{1},{2},{3},{2,3}}
%e A326971                               {{1},{2},{1,3},{2,3}}
%e A326971                               {{1},{2},{3},{1,2,3}}
%e A326971                               {{3},{1,2},{1,3},{2,3}}
%e A326971                               {{1},{2},{3},{1,3},{2,3}}
%e A326971                               {{1,2},{1,3},{2,3},{1,2,3}}
%e A326971                               {{1},{2},{3},{2,3},{1,2,3}}
%e A326971                               {{2},{3},{1,2},{1,3},{2,3}}
%e A326971                               {{1},{2},{1,3},{2,3},{1,2,3}}
%e A326971                               {{1},{2},{3},{1,2},{1,3},{2,3}}
%e A326971                               {{3},{1,2},{1,3},{2,3},{1,2,3}}
%e A326971                               {{1},{2},{3},{1,3},{2,3},{1,2,3}}
%e A326971                               {{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%e A326971                               {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%Y A326971 Unlabeled set-systems are A000612.
%Y A326971 Unlabeled set-systems whose dual is strict are A326946.
%Y A326971 The labeled version is A326968.
%Y A326971 The version with empty edges allowed is A326969.
%Y A326971 The T_0 case (with strict dual) is A326972.
%Y A326971 The covering case is A326973 (first differences).
%Y A326971 Cf. A319559, A326951, A326965, A326966, A326970, A326974, A326975, A326978.
%K A326971 nonn,more
%O A326971 0,2
%A A326971 _Gus Wiseman_, Aug 10 2019