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 A358455 #7 Nov 18 2022 21:53:03
%S A358455 1,1,2,4,10,26,72,206,608,1830,5612,17442,54866,174252,558072,1800098
%N A358455 Number of recursively anti-transitive ordered rooted trees with n nodes.
%C A358455 We define an unlabeled ordered rooted tree to be recursively anti-transitive if no branch of a branch of a subtree is a branch of the same subtree farther to the left.
%e A358455 The a(1) = 1 through a(5) = 10 trees:
%e A358455 o (o) (oo) (ooo) (oooo)
%e A358455 ((o)) ((o)o) ((o)oo)
%e A358455 ((oo)) ((oo)o)
%e A358455 (((o))) ((ooo))
%e A358455 (((o))o)
%e A358455 (((o)o))
%e A358455 (((oo)))
%e A358455 ((o)(o))
%e A358455 (o((o)))
%e A358455 ((((o))))
%t A358455 aot[n_]:=If[n==1,{{}},Join@@Table[Tuples[aot/@c],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
%t A358455 Table[Length[Select[aot[n],FreeQ[#,{___,x_,___,{___,x_,___},___}]&]],{n,10}]
%Y A358455 The unordered version is A324765, ranked by A324766.
%Y A358455 The undirected version is A358456.
%Y A358455 A000108 counts ordered rooted trees, unordered A000081.
%Y A358455 A306844 counts anti-transitive rooted trees.
%Y A358455 A358453 counts transitive ordered trees, unordered A290689.
%Y A358455 Cf. A318185, A324695, A324751, A324756, A324758, A324764, A324767, A324768, A324838, A324840, A324844.
%K A358455 nonn,more
%O A358455 1,3
%A A358455 _Gus Wiseman_, Nov 18 2022