This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279863 #5 Dec 21 2016 11:06:13
%S A279863 0,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,2,2,1,1,4,3,4,2,5,6,10,8,11,11,20,
%T A279863 22,29,36,45,53,77,83,108,141,172,208,274,323
%N A279863 Number of maximal transitive finitary sets with n brackets.
%C A279863 A finitary set is transitive if every element is also a subset. A set system is maximal if the union is also a member.
%H A279863 Gus Wiseman, <a href="/A279863/a279863.png">Maximal transitive identity trees up to n=25</a>
%e A279863 The a(23)=3 maximal transitive finitary sets are:
%e A279863 (()(())(()(()))((())(()(())))(()(())(()(())))),
%e A279863 (()(())((()))(((())))(()((())))(()(())((())))),
%e A279863 (()(())((()))(()(()))(()((())))(()(())((())))).
%t A279863 maxtransfins[n_]:=If[n===1,{},Select[Union@@FixedPointList[Complement[Union@@Function[fin,Cases[Complement[Subsets[fin],fin],sub_:>With[{nov=Sort[Append[fin,sub]]},nov/;Count[Union[nov,{Union@@nov}],_List,{0,Infinity}]<=n]]]/@#,#]&,{{}}],And[Count[#,_List,{0,Infinity}]===n,MemberQ[#,Union@@#]]&]];
%t A279863 Table[Length[maxtransfins[n]],{n,20}]
%Y A279863 Cf. A001192, A004111, A276625, A279065, A279614, A279861.
%K A279863 nonn
%O A279863 1,18
%A A279863 _Gus Wiseman_, Dec 21 2016