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 A132054 #5 Jan 05 2021 22:07:32 %S A132054 1,135,11385,782595,48455550,2839726890,162006594750,9153448954650, %T A132054 517901415206175,29561484489161625,1710820788894392175, %U A132054 100736227863519373125,6049367893509827386500,371102130337105087420500 %N A132054 Ninth column of triangle A035342. %C A132054 a(n), n >= 9, enumerates unordered forests composed of nine 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 A132054 E.g.f.: ((x*c(x/2)*(1-2*x)^(-1/2))^9)/9!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0. %F A132054 E.g.f.: (-1+(1-2*x)^(-1/2))^9/9!. %e A132054 a(10)=135=3*binomial(10,2) increasing ternary 9-forest with n=10 vertices: there are three 9-forests (eight 1-vertex trees together with any of the three different 2-vertex trees) each with binomial(10,2)= 45 increasing labelings. %Y A132054 Cf. A132053 (eighth column). %K A132054 nonn,easy %O A132054 9,2 %A A132054 _Wolfdieter Lang_ Sep 14 2007