I am planning an introductory combinatorics course (mixed grad-undergrad) and am trying to decide whether it is worth budgeting a day for [Lagrange inversion][1]. The reason I hesitate is that I know of very few applications for it -- basically just enumeration of trees and some slight variants on this. I checked *van Lint and Wilson*, *Enumerative Combinatorics II* (but not the exercises) and *Concrete Mathematics*, and they all only present this application.

So, besides counting trees, where can we use Lagrange inversion? 


  [1]: http://en.wikipedia.org/wiki/Lagrange_inversion_theorem