Generating functions for moments of the quasi-nilpotent ${\rm DT}$-operator
Ken Dykema and Catherine Yan
We prove a recursion formula for generating functions of certain renormalizations of $*$-moments of the ${\rm DT}(\delta_0,1)$-operator $T$, involving an operation $\odot$ on formal power series and a transformation $\mathcal E$ that converts $\odot$ to usual multiplication. This recursion formula is used to prove that all of these generating functions are rational functions, and to find a few of them explicitly.