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 A097391 #17 Feb 13 2025 08:30:51 %S A097391 0,1,3,8,17,37,71,138,252,458 %N A097391 The number of hierarchies of n labeled elements with at least one subhierarchy composed of exactly 2 levels and no subhierarchy with more than 2 levels. %C A097391 Conjectured to be (A378854) /3. - _Wouter Meeussen_, Feb 10 2025 %H A097391 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 A097391 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) = 17 hierarchies where at least one subhierarchy has exactly 2 levels (and no level l > 2 is allowed): %e A097391 4|1; 1|4; 3|2; 2|3; 2|2:1; 2|1:2; 1|2:2; 2|1:1|1; 1|2:1|1; 2|1:1:1; 1|2:1:1; 1|1:1:1:1; 1|3:1; 3|1:1; 1|1:2:1; 1|1:1|1:1; 1|1:3. %Y A097391 Cf. A034691, A097237, A097392, A000041, A378854. %K A097391 nonn,more %O A097391 1,3 %A A097391 _Thomas Wieder_, Aug 13 2004