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 A358453 #9 Nov 18 2022 21:53:07
%S A358453 1,1,1,2,4,8,17,37,83,190,444,1051,2518,6090,14852
%N A358453 Number of transitive ordered rooted trees with n nodes.
%C A358453 We define an unlabeled ordered rooted tree to be transitive if every branch of a branch of the root already appears farther to the left as a branch of the root. An undirected version is A358454.
%e A358453 The a(1) = 1 through a(7) = 17 trees:
%e A358453 o (o) (oo) (ooo) (oooo) (ooooo) (oooooo)
%e A358453 (o(o)) (o(o)o) (o(o)oo) (o(o)ooo)
%e A358453 (o(oo)) (o(oo)o) (o(oo)oo)
%e A358453 (oo(o)) (o(ooo)) (o(ooo)o)
%e A358453 (oo(o)o) (o(oooo))
%e A358453 (oo(oo)) (oo(o)oo)
%e A358453 (ooo(o)) (oo(oo)o)
%e A358453 (o(o)(o)) (oo(ooo))
%e A358453 (ooo(o)o)
%e A358453 (ooo(oo))
%e A358453 (oooo(o))
%e A358453 (o(o)(o)o)
%e A358453 (o(o)(oo))
%e A358453 (o(o)o(o))
%e A358453 (o(oo)(o))
%e A358453 (oo(o)(o))
%e A358453 (o(o)((o)))
%t A358453 aot[n_]:=If[n==1,{{}},Join@@Table[Tuples[aot/@c],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
%t A358453 Table[Length[Select[aot[n],Function[t,And@@Table[Complement[t[[k]],Take[t,k]]=={},{k,Length[t]}]]]],{n,10}]
%Y A358453 The unordered version is A290689, ranked by A290822.
%Y A358453 The undirected version is A358454, ranked by A358458.
%Y A358453 These trees are ranked by A358457.
%Y A358453 A000081 counts rooted trees.
%Y A358453 A306844 counts anti-transitive rooted trees.
%Y A358453 Cf. A318185, A324695, A324751, A324756, A324758, A324764-A324768, A324838, A324840, A324844, A358456.
%K A358453 nonn,more
%O A358453 1,4
%A A358453 _Gus Wiseman_, Nov 18 2022