  We analyze the sequence of polynomials defined by the differential-difference
equation $P_{n+1}(x)=P_{n}^{\prime}(x)+x(n+1)P_{n}(x)$ asymptotically as
$n\to\infty$. The polynomials $P_{n}(x)$ arise in the computation of higher
derivatives of the inverse error function $\operatorname{inverf}(x)$. We use
singularity analysis and discrete versions of the WKB and ray methods and give
numerical results showing the accuracy of our formulas.
