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%I #5 Jan 05 2021 22:07:32
%S 1,135,11385,782595,48455550,2839726890,162006594750,9153448954650,
%T 517901415206175,29561484489161625,1710820788894392175,
%U 100736227863519373125,6049367893509827386500,371102130337105087420500
%N Ninth column of triangle A035342.
%C 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 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 E.g.f.: (-1+(1-2*x)^(-1/2))^9/9!.
%e a(10)=135=3*binomial(10,2) increasing ternary 9-forest with n=10 vertices: there are three 9-forests (eight 1-vertex trees together with any of the three different 2-vertex trees) each with binomial(10,2)= 45 increasing labelings.
%Y Cf. A132053 (eighth column).
%K nonn,easy
%O 9,2
%A _Wolfdieter Lang_ Sep 14 2007
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