Q-factorial

The q-factorial is the q-analog of the factorial, based on the q-gamma function. It is written $$[n]_q!$$ or $$\mathrm{faq}(n,q)$$ and is defined as

$$[n]_q! = \prod^{n - 1}_{i = 0} \left(\sum^{i}_{j = 0} q^j\right) = q^0 \cdot \left(q^0 + q^1\right) \cdot \left(q^0 + q^1 + q^2\right) \cdot \ldots \cdot \left(q^0 + q^1 + \ldots + q^{n - 1}\right)$$.