# Irreducibility of q-factorial plus 1

Let $$q$$ be a formal variable and for every positive integer $$n$$ let $$[n]_q! = 1 (1 + q)(1 + q + q^2) \cdots (1 + q + \cdots + q^{n-1})$$ 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 $$n = 117$$.