\displaystyle \sum_{m=0}^\infty \Bigl(\frac{q^{m+1}-1}{q-1}\Bigr)^k t^m = \frac{\sum_{\pi} q^{\mathrm{comaj}(\pi)} t^{\mathrm{des}(\pi)}}{(1-t)(1-qt)\ldots (1-q^k t)}.