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