How to calculate A-Hilb $CC^n$ for $1/r(a,b,1,\dots,1)$

An elementary result says (in the coprime case) that the $n$-dimensional Gorenstein quotient $A=1/r(a,b,1,\dots,1)$ (with 1 repeated $n-2$ times) has a crepant resolution if and only if the point nearest the ($x_1=0$) face is $P_c=1/r(1,d,c,\dots,c)$ where $d=r-(n-2)c-1>0$, and every entry of the Hirzebruch-Jung continued fraction of $r/d$ is congruent to $2\;\operatorname{mod} n-2$. In these cases a modification of the Nakamura-Craw-Reid algorithm calculates the A-Hilbert scheme, with some fun for large $n$. This talk is based on joint work with Sarah Davis and Timothy Logvinenko and overlaps in part with Chapter 4 of Sarah Davis's 2011 Warwick PhD thesis.