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%I #5 Oct 07 2019 14:10:12
%S 1,165,16665,1349205,97026930,6526750230,423076603950,26922666320550,
%T 1702498733310375,107876426221438875,6888889247523458175,
%U 445180690239692281875,29198763785973826044000
%N Tenth column of triangle A035342.
%C a(n), n>=10, enumerates unordered forests composed of nine plane 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.
%C a(n), n>=10, enumerates unordered forests composed of ten 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))^10)/10!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.
%F E.g.f.: (-1+(1-2*x)^(-1/2))^10/10!.
%e a(11)=165=3*binomial(11,2) increasing ternary 10-forest with n=11 vertices: there are three 10-forests (nine one vertex trees together with any of the three different 2-vertex trees) each with binomial(11,2)= 55 increasing labelings.
%Y Cf. A132054 (eighth column).
%K nonn,easy
%O 10,2
%A _Wolfdieter Lang_ Sep 14 2007
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