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Eighth column of triangle A035342.
1

%I #5 Jan 05 2021 22:05:56

%S 1,108,7470,429660,22629915,1143782640,56936699820,2835191759400,

%T 142610008065525,7291723635296100,380553986882119050,

%U 20327650785482940900,1113292728197378103375,62584367768103890709000

%N Eighth column of triangle A035342.

%C a(n), n >= 8, enumerates unordered forests composed of eight 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))^8)/8!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.

%F E.g.f.: (-1+(1-2*x)^(-1/2))^8/8!.

%e a(9)=108=3*binomial(9,2) increasing ternary 8-forest with n=9 vertices: there are three 8-forests (seven 1-vertex trees together with any of the three different 2-vertex trees) each with binomial(9,2)= 36 increasing labelings.

%Y Cf. A132052 (seventh column).

%K nonn,easy

%O 8,2

%A _Wolfdieter Lang_ Sep 14 2007