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 A097392 #14 Feb 11 2025 02:28:32 %S A097392 0,0,1,4,12,32,78,183,408,886 %N A097392 The number of hierarchies of n labeled elements with at least one subhierarchy composed of exactly 3 levels and no subhierarchy with more than 3 levels. %H A097392 N. J. A. Sloane and Thomas Wieder, <a href="https://arxiv.org/abs/math/0307064">The Number of Hierarchical Orderings</a>, arXiv:math/0307064 [math.CO], 2003; Order 21 (2004), 83-89. %e A097392 Let : denote the separation between two subhierarchies, e.g. 2:3 are two subhierarchies where subhierarchy s=1 contains two elements and subhierarchy s=2 contains three elements. Let | denote the separation between two levels, e.g. 2|2|1 is a hierarchy composed of three levels with two elements on levels l=1 and l=2 and one element on level l=3. For n=5 one has a(5) = 12 hierarchies where at least one subhierarchy has exactly 3 levels (and no level l > 3 is allowed): %e A097392 3|1|1; 1|3|1; 1|1|3; 2|2|1; 2|1|2; 1|2|2; 1|1|1:2; 1|1|1:1:1; 1|1|1:1|1; 2|1|1:1; 1|2|1:1; 1|1|2:1. %Y A097392 Cf. A034691, A097237, A097391, A000041. %K A097392 nonn,more %O A097392 1,4 %A A097392 _Thomas Wieder_, Aug 13 2004