The limiting distribution of the qq-derangement numbers

We prove the normality of the limiting distribution of the coefficients of the qq-derangement numbers of type BB based on the formula of Foata and Han that contains a parameter zz. Setting the parameter zz to zero, we are led to the case of ordinary qq-derangement numbers. For z=1z=1, we obtain the normality of the limiting distribution of the coefficients of the usual qq-derangement numbers of type BB.