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 A358553 #8 Nov 27 2022 08:56:32
%S A358553 0,1,2,1,3,2,2,1,2,3,3,2,3,2,2,1,4,2,4,3,4,3,3,2,2,3,3,2,3,2,2,1,3,4,
%T A358553 3,2,5,4,4,3,3,4,4,3,4,3,3,2,4,2,4,3,4,3,3,2,2,3,3,2,3,2,2,1,3,3,5,4,
%U A358553 4,3,3,2,4,5,5,4,5,4,4,3,5,3,5,4,5,4,4
%N A358553 Number of internal (non-leaf) nodes in the n-th standard ordered rooted tree.
%C A358553 We define the n-th standard ordered rooted tree to be obtained by taking the (n-1)-th composition in standard order (graded reverse-lexicographic, A066099) as root and replacing each part with its own standard ordered rooted tree. This ranking is an ordered variation of Matula-Goebel numbers, giving a bijective correspondence between positive integers and unlabeled ordered rooted trees.
%e A358553 The 89-th standard rooted tree is ((o)o(oo)), and it has 3 internal nodes, so a(89) = 3.
%t A358553 stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t A358553 srt[n_]:=If[n==1,{},srt/@stc[n-1]];
%t A358553 Table[Count[srt[n],_[__],{0,Infinity}],{n,100}]
%Y A358553 This statistic is counted by A001263, unordered A358575 (reverse A055277).
%Y A358553 The unordered version is A342507, firsts A358554.
%Y A358553 Other statistics: A358371 (leaves), A358372 (nodes), A358379 (edge-height).
%Y A358553 A000081 counts rooted trees, ordered A000108.
%Y A358553 Cf. A000891, A014221, A358373, A358585, A358586, A358588.
%K A358553 nonn
%O A358553 1,3
%A A358553 _Gus Wiseman_, Nov 26 2022