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 A131449 #12 Aug 29 2019 08:52:29 %S A131449 1,1,2,1,6,3,3,2,1,24,12,12,12,8,8,6,6,4,4,3,3,2,1,120,60,60,60,60,40, %T A131449 40,40,30,30,30,30,30,24,20,20,20,20,20,15,15,15,15,12,12,12,10,10,10, %U A131449 10,8,8,6,6,5,5,4,4,3,3,2,1,720 %N A131449 Number of organic (also called increasing) vertex labelings of rooted ordered trees with n non-root vertices. %C A131449 Organic vertex labeling with numbers 1,2,...,n means that the sequence of vertex labels along the (unique) path from the root with label 0 to any leaf (non-root vertex of degree 1) is increasing. %C A131449 Row lengths sequence, i.e. the number of rooted ordered trees, C(n):=A000108(n) (Catalan numbers): [1,1,2,5,14,42,...]. %C A131449 Number of rooted trees with n non-root vertices [1,1,2,4,9,20,...]=A000081(n+1). %C A131449 Row sums give [1,1,3,155,105,945,...]= A001147(n), n>=0. A035342(n,1), n>=1, first column of triangle S2(3). %H A131449 W. Lang, <a href="/A131449/a131449.txt">First 6 rows</a>. %H A131449 W. Lang, <a href="/A131449/a131449fig5.pdf">Rooted ordered trees with n=5 non-root vertices and number of labelings</a>. %e A131449 [0! ]; [1! ]; [2!,1]; [3!,3,3,2,1], [4!,12,12,12,8,8,6,6,4,4,3,3,2,1];... %e A131449 n=3: 3 labelings (0,1,2)(0,3), (0,1,3) (0,2) and (0,2,3) (0,1) for the rooted tree o-o-x-o. %e A131449 n=3: 3 labelings (0,3)(0,1,2), (0,2)(0,1,3) and (0,1)(0,2,3) for the rooted tree o-x-o-o. %K A131449 nonn,more,tabf %O A131449 0,3 %A A131449 _Wolfdieter Lang_, Aug 07 2007