E.A. Potekhina

Improved management of industrial and defense sector of the country requires the automation of the collection and processing of information, development of administrative decisions in a limited time frame. This leads to the emergence of new and more complex scientific problems whose solution is the traditional formal methods are not always possible. In particular, the solution of multidimensional and semistructured problems necessitates the use of combinatorial optimization algorithms. It is therefore proposed to consider the decision of one of combinatorial and probabilistic problems through the application of the oscillating random walk. Louis W. Shapiro gave a combinatorial proof of a bilinear generating function for Chebyshev polynomials. In a similar way, Jong H. Kim received some generalization of Shapiro-s results. In this article using the oscillating random walk, we obtained the general solution of the problem of weighted ordered partitions generating function calculation. Previously known combinatorial methods to solve this problem give results only in particular cases.