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 A071214 #14 Jan 04 2021 20:25:53
%S A071214 1,5,46,614,10716,230712,5903472,174942000,5890370400,222069752640,
%T A071214 9265980286080,423888544154880,21094789126924800,1134492559101619200,
%U A071214 65567415318776985600,4052502049455940147200,266725354163752808755200,18624661769541550593024000
%N A071214 Number of labeled ordered trees with n nodes such that the root is smaller than all its children.
%D A071214 C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees, research report RR-1226-99, LaBRI, Bordeaux I University, 1999.
%H A071214 C. Chauve, S. Dulucq and O. Guibert, <a href="http://www.cecm.sfu.ca/~cchauve/Publications/SFCA00.ps">Enumeration of some labelled trees</a>, FPSAC 2000, pp. 146-157. 2000.
%F A071214 From _Vladimir Kruchinin_, Jun 02 2016: (Start)
%F A071214 E.g.f.: -[(log(1-x*C(x)))/C(x)]', where C(x) is g.f. of Catalan numbers (A000108).
%F A071214 a(n) = ((n+1)!*Sum_{k=1..n} ((k*binomial(2*n-k-1,n-k))/(k+1)))/n. (End)
%p A071214 a:= n -> ((2*n-2)! / (n-1)!) - sum((n+k-1)! / ((n-k-1)*k!), k=0 .. n-2):
%p A071214 seq(a(n), n=2..22);
%Y A071214 Cf. A000312, A000108.
%K A071214 easy,nonn
%O A071214 2,2
%A A071214 Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002