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%I #7 Mar 31 2012 13:19:58
%S 0,0,0,0,1,45,1470,43890,1291815,38710035,1199167200,38692476900,
%T 1304976397725,46070080281225,1702810398539250,65862570279255750,
%U 2663551451057371875,112503209942059311375,4957166849516125744500
%N Fifth column of triangle A035342; related to A035330.
%C a(n) = A035342(n,5).
%C a(n), n>=5, enumerates unordered n-vertex forests composed of five plane (ordered) increasingly labeled ternary (3-ary) trees. 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 a(n) = n!*A035330(n-4)/(5!*2^(n-5)), n >= 5; E.g.f. ((x*c(x/2)*(1-2*x)^(-1/2))^5)/5!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.
%e a(6)=45 increasing ternary 5-forest with n=6 vertices: there are three such 5-forests (four one vertex trees together with any of the three different 2-vertex trees) each with binomial(6,2)= 15 increasing labelings. W. Lang, Sep 14 2007.
%Y Cf. A000108, A035342, A035330.
%K easy,nonn
%O 1,6
%A _Wolfdieter Lang_
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