Let $q$ be a formal variable and for every positive integer $n$ let $$[n]_q! = 1 (1 + q)(1 + q + q^2) \dotsm (1 + q + \dotsb + q^{n-1})$$ be the $q$-factorial.
Is it true that $[n]_q! + 1$ is an irreducible polynomial over $\mathbb{Z}$ for all positive integers $n$?
I already asked this question on MSE, and Sil verified it up to $n = 117$.