This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A035520 #10 Jul 21 2016 12:18:30 %S A035520 0,0,0,1,30,705,15960,370125,8998290,231416325,6314962500, %T A035520 182894567625,5615811951750,182497749258825,6264206330382000, %U A035520 226636350724909125,8624703350821808250,344535241891693978125,14419858385821910521500 %N A035520 Fourth column of triangle A035342; related to A045894. %C A035520 a(n) = A035342(n,4). %C A035520 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 A035520 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 A035520 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 A035520 Cf. A035342, A045894. %K A035520 easy,nonn %O A035520 1,5 %A A035520 _Wolfdieter Lang_