%I A132054
%S A132054 1,135,11385,782595,48455550,2839726890,162006594750,9153448954650,
%T A132054 517901415206175,29561484489161625,1710820788894392175,
%U A132054 100736227863519373125,6049367893509827386500,371102130337105087420500
%N A132054 Ninth column of triangle A035342.
%C A132054 a(n), n>=9, enumerates unordered forests composed of nine plane increasing 
               ternary trees with n vertices. See A001147 (number of increasing 
               ternary trees) and a D. Callan comment there. For a picture of some 
               ternary trees see a W. Lang link under A001764.
%F A132054 E.g.f. ((x*c(x/2)*(1-2*x)^(-1/2))^9)/9!, where c(x) = g.f. for Catalan 
               numbers A000108, a(0) := 0.
%F A132054 E.g.f. (-1+(1-2*x)^(-1/2))^9/9!.
%e A132054 a(10)=135=3*binomial(10,2) increasing ternary 9-forest with n=10 vertices: 
               there are three 9-forests (eight one vertex trees together with any 
               of the three different 2-vertex trees) each with binomial(10,2)= 
               45 increasing labelings.
%Y A132054 Cf. A132053 (eighth column).
%Y A132054 Sequence in context: A143404 A051028 A076011 this_sequence A106175 A051307 
               A056740
%Y A132054 Adjacent sequences: A132051 A132052 A132053 this_sequence A132055 A132056 
               A132057
%K A132054 nonn,easy
%O A132054 9,2
%A A132054 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Sep 14 2007