A few years ago I [computed][1] the Tutte polynomials of the matroids given by the classical Coxeter groups, and found that their generating functions are all simple variations of the series $\sum_n x^n y^{n^2}$, which I swear I saw in my analysis classes years ago. :) 
I've wondered if there is a more geometric/algebraic explanation of this. Is this series known? Are there other natural occurrences of it that might be relevant? 


  [1]: http://math.sfsu.edu/federico/Articles/arrangem.pdf