Project Euler 176 - Right-angled triangles that share a cathetus

Official link: https://projecteuler.net/problem=176

Thought Process

Warning: This problem is not suitable for hints, don't look further if you don't want to be spoiled!

I actually found http://oeis.org/A046079 and you will see the formula I derived below is listed and reverse engineered the whole problem without writing a single line of code, felt a bit nasty doing that, so below is my proof (If it's not the standard proof) of how to get the answer!