Non-equivalent Ternary Tree.

After several weeks' study on induction prove. I gotta a better sense about the ternary tree question than I was first time doing assignment 1. This question is interesting now. I checked some books about the property of trees. I kinda found a closed form formula for this question. which is 3n!/(2n!n!(2n+1)). However, It is kinda not that easy to prove. My way to solve this problem is using Sigma for different trees and get the product of them. It is sound silly comparing to that perfectly closed form formula, but it is easy to proof, and understand.