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 A358454 #5 Nov 18 2022 21:53:11
%S A358454 1,1,1,3,6,13,33,80,201,509,1330,3432,8982,23559,62189
%N A358454 Number of weakly transitive ordered rooted trees with n nodes.
%C A358454 We define an unlabeled ordered rooted tree to be weakly transitive if every branch of a branch of the root is itself a branch of the root.
%e A358454 The a(1) = 1 through a(6) = 13 trees:
%e A358454 o (o) (oo) (ooo) (oooo) (ooooo)
%e A358454 ((o)o) ((o)oo) ((o)ooo)
%e A358454 (o(o)) ((oo)o) ((oo)oo)
%e A358454 (o(o)o) ((ooo)o)
%e A358454 (o(oo)) (o(o)oo)
%e A358454 (oo(o)) (o(oo)o)
%e A358454 (o(ooo))
%e A358454 (oo(o)o)
%e A358454 (oo(oo))
%e A358454 (ooo(o))
%e A358454 ((o)(o)o)
%e A358454 ((o)o(o))
%e A358454 (o(o)(o))
%t A358454 aot[n_]:=If[n==1,{{}},Join@@Table[Tuples[aot/@c],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
%t A358454 Table[Length[Select[aot[n],Complement[Union@@#,#]=={}&]],{n,10}]
%Y A358454 The unordered version is A290689, ranked by A290822.
%Y A358454 The directed version is A358453.
%Y A358454 A000081 counts rooted trees.
%Y A358454 A306844 counts anti-transitive rooted trees.
%Y A358454 Cf. A318185, A324695, A324751, A324756, A324758, A324764-A324768, A324838, A324840, A324844, A358456.
%K A358454 nonn,more
%O A358454 1,4
%A A358454 _Gus Wiseman_, Nov 18 2022