%I #11 Jan 05 2020 12:03:02
%S 1,2,3,10,899
%N Number of non-isomorphic fully chiral set-systems on n vertices.
%C A set-system is a finite set of finite nonempty sets. It is fully chiral if every permutation of the covered vertices gives a different representative.
%e Non-isomorphic representatives of the a(0) = 1 through a(3) = 10 set-systems:
%e 0 0 0 0
%e {1} {1} {1}
%e {2}{12} {2}{12}
%e {1}{3}{23}
%e {2}{13}{23}
%e {3}{23}{123}
%e {2}{3}{13}{23}
%e {1}{3}{23}{123}
%e {2}{13}{23}{123}
%e {2}{3}{13}{23}{123}
%Y The labeled version is A330282.
%Y Partial sums of A330295 (the covering case).
%Y Unlabeled costrict (or T_0) set-systems are A326946.
%Y BII-numbers of fully chiral set-systems are A330226.
%Y Non-isomorphic fully chiral multiset partitions are A330227.
%Y Fully chiral partitions are A330228.
%Y Fully chiral factorizations are A330235.
%Y MM-numbers of fully chiral multisets of multisets are A330236.
%Y Cf. A000612, A016031, A055621, A083323, A283877, A319637, A330098, A330231, A330232, A330234.
%K nonn,more
%O 0,2
%A _Gus Wiseman_, Dec 10 2019