While doing some work in geometric representation theory I have come across the following sequence of polynomials in two variables $(q,x)$ which I would like to denote by $n!_{q,x}$. For small $n$ these polynomials look as follows:

$2!_{x,q}=x+q$

$3!_{x,q}=x^3+x^2(q^2+q)+x(q^2+q)+q^3$

$$ 4!_{x,q}=x^6+x^5(q^3+q^2+q)+x^4(q^4+q^3+2q^2+q)+x^3(q^5+q^4+2q^3+q^2+q)+ $$ $$ x^2(q^5+2q^4+q^3+q^2)+x(q^5+q^4+q^3)+q^6 $$

The polynomials are actually symmetric in $q$ and $x$ and when one puts $x=1$ one recovers the usual $q$-analog of $n!$ (in particular, when both $q$ and $x$ are 1, we get $n!$).

My question is this: has anybody seen such polynomials before? What is the correct definition of those polynomials for general $n$? Any information will be greatly appreciated.