Clark–Ismail coefficient-positivity conjecture for the power series of $g_j$

For $j>1$, define

$$g_j(v)=\left(\frac{1-\operatorname{e}^{-v}}{v}\right)^{j+1}\operatorname{e}^{jv}\frac{\operatorname{d}^j}{\operatorname{d}v^j}\left(\frac{v^j}{1-\operatorname{e}^{-v}}\right).$$

Suppose that $g_j$ has the power-series expansion

$$g_j(v)=\sum_{k=0}^{\infty}\gamma(j,k)v^k.$$

Clark–Ismail's coefficient-positivity conjecture. Then $\gamma(j,k)\ge0$ for all $j>1$ and $k\ge0$. This is a coefficientwise strengthening of the positivity question for $g_j$ and was posed alongside the preceding conjecture; the source does not specify whether it has been resolved.