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%I #10 Jul 21 2016 12:18:30
%S 0,0,0,1,30,705,15960,370125,8998290,231416325,6314962500,
%T 182894567625,5615811951750,182497749258825,6264206330382000,
%U 226636350724909125,8624703350821808250,344535241891693978125,14419858385821910521500
%N Fourth column of triangle A035342; related to A045894.
%C a(n) = A035342(n,4).
%C a(n), n>=4, enumerates unordered n-vertex forests composed of four 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!*A045894(n-4)/(4!*2^(n-4)), n >= 4; E.g.f. ((x*c(x/2)/(1-2*x)^(1/2))^4)/4!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.
%e a(5)=30 increasing ternary 4-forest with n=5 vertices: there are three such 4-forests (three one vertex trees together with any of the three different 2-vertex trees) each with 10 increasing labelings. _Wolfdieter Lang_, Sep 14 2007.
%Y Cf. A035342, A045894.
%K easy,nonn
%O 1,5
%A _Wolfdieter Lang_
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