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.
For n = 5, the tree is
0
/ \
1 2
/ \
3 4
Pre-order traversal is vertices {0,1,3,4,2} and among the permutations of 0..4 this has rank a(5) = 3.
a[n_Integer]:=Module[{res={}, data, len}, data=Range[n]; len=Length[data]; Which[MemberQ[{1, 2, 3}, n], 0, n==4, 1,True, DepthFirstScan[TreeGraph[Table[Floor[j/2]->j, {j, 2, len}]], 1,{"PrevisitVertex"->(AppendTo[res, #]&)}]; ResourceFunction["PermutationIndex"][res]-1]]; a/@Range[1, 25] (* Shenghui Yang, Feb 15 2025 *)
from binarytree import Node, build from sympy.combinatorics import Permutation a = lambda n: Permutation([node.value for node in build(list(range(n))).preorder]).rank() print([a(n) for n in range(1,26)])
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