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 A358460 #7 Nov 19 2022 08:57:07
%S A358460 1,1,2,5,13,36,103,301,902,2767,8637,27324,87409,282319,919352
%N A358460 Number of locally disjoint ordered rooted trees with n nodes.
%C A358460 Locally disjoint means no branch of any vertex overlaps a different (unequal) branch of the same vertex.
%e A358460 The a(1) = 1 through a(5) = 13 trees:
%e A358460 o (o) (oo) (ooo) (oooo)
%e A358460 ((o)) ((o)o) ((o)oo)
%e A358460 ((oo)) ((oo)o)
%e A358460 (o(o)) ((ooo))
%e A358460 (((o))) (o(o)o)
%e A358460 (o(oo))
%e A358460 (oo(o))
%e A358460 (((o))o)
%e A358460 (((o)o))
%e A358460 (((oo)))
%e A358460 ((o(o)))
%e A358460 (o((o)))
%e A358460 ((((o))))
%t A358460 aot[n_]:=If[n==1,{{}},Join @@ Table[Tuples[aot/@c],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
%t A358460 Table[Length[Select[aot[n],FreeQ[#,{___,{___,x_,___},___,{___,x_,___},___}]&]],{n,10}]
%Y A358460 The locally non-intersecting version is A143363, unordered A007562.
%Y A358460 The unordered version is A316473, ranked by A316495.
%Y A358460 A000108 counts ordered rooted trees, unordered A000081.
%Y A358460 A358453 counts transitive ordered trees, unordered A290689.
%Y A358460 Cf. A006013, A302696, A316471, A316694, A318185, A319378, A324768, A324844.
%K A358460 nonn,more
%O A358460 1,3
%A A358460 _Gus Wiseman_, Nov 19 2022