Author(s)

Beih S. El-Desouky¹, Abdelfattah Mustafa¹, E. M. Mahmoud²

¹Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt.
²Mathematics Department, Faculty of Science, Aswan University, Aswan, Egypt.

Khidr and El-Desouky [1] derived a symmetric sum involving the Stirling numbers of the first kind through the process of counting the number of paths along a rectangular array n*m denoted by  A_nm. We investigate the generating function for the general case and hence some special cases as well. The probability function of the number of paths along is obtained. Moreover, the moment generating function of the random variable X and hence the mean and variance are obtained. Finally, some applications are introduced.

Stirling Numbers, Generating Function, Moment Generating Function, Comtet Numbers, Maple Program

El-Desouky, B. , Mustafa, A. and Mahmoud, E. (2015) Some New Results on the Number of Paths. Open Journal of Modelling and Simulation, 3, 63-69. doi: 10.4236/ojmsi.2015.33007.