After a bit longer than I anticipated, I’ve posted a new article. This one is a followup to the previous article on generating functions, although you should be able to follow it just fine if you even just the definition of generating functions. It’s about an application of generating functions to the question of counting objects called ``integer partitions,’’ culminating in a proof of a beautiful result called the Pentagonal Number Theorem.

This article grew out of an activity that I ran last year for my students at New York Math Circle, and it’s one of my favorite arguments in all of combinatorics. Nothing in this presentation is especially original — you can find essentially the same proof on Wikipedia — but if you enjoyed the first generating function article and want to read more in the same style, I hope you enjoy this one as well.