The limiting distribution of the -derangement numbers

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