## Generating functions, Tutte polynomials, and the bivariate series $\sum_n x^n y^{n^2} / n!$.

A few years ago I computed 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 $\sum_n \frac{x^n y^{n^2}}{n!}$. 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?

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en.wikipedia.org/wiki/Theta_function – Qiaochu Yuan Jul 3 at 0:58
Don't you mean $\sum_n x^n y^{n^2}/n!$? – Ira Gessel Jul 3 at 13:39
Is it known whether $\sum x^n y^{n^2} / {n!}$ satisfies an ADE? – Martin Rubey Jul 3 at 17:03
The generating function $f(x) = \sum_n x^n y^\binom{n}{2}/n!$ satisfies $f'(x) = f(xy)$. – Ira Gessel Jul 3 at 17:17
Ira, I did mean that, and I corrected it in the post. (I hope that's proper math overflow etiquette.) – Federico Ardila Jul 3 at 17:58
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