Enumeration of symplectic and orthogonal injective partial transformations

In this paper, we compute the generating function of sn=∑i=0naini2i!, where a   is a real number with a≥1a≥1. We then use this function to determine the generating functions of the symplectic and orthogonal Renner monoids. Furthermore, we show that these functions are closely related to Laguerre polynomials.