Application Of Generating Function And Riordan Array In Special Combination Sequence

Firstly,we give the definitions of the generating functions of degenerate type 2Changhee sequences and higher-order type 2 Changhee sequences by generalizing the generating function of type 2 Changhee sequences,and their properties are deduced by using the generating function method.Secondly,the combinatorial identities of the degenerate type 2 Changhee polynomials,higher order type 2 Changhee polynomials and special combinatorial sequences are concluded by applying the method of Riordan array and combinatorial inversion.The main work is as follows:1.The type 2 Changhee polynomials are generalized,then the related combinatorial identities of type 2 Changhee polynomials and Changhee-central sequence,Bell polynomials,type 2 Changhee polynomials,Stirling Numbers are established by using Riordan array method.Some properties of degenerate type 2 Changhee phoynomials are obtained by using the generation function method.2.Some basic properties of higher-order type 2 Changhee polynomials are given by using the method of generating function.We apply the Riordan array lemma to study the identities between the higher-order type 2 Changhee polynomials and special combinatorial sequences of the generalized Lah polynomials,generalized Stirling polynomial,the generalized Bell polynomial.Therefore new combinatorial identities of the higher-order type 2 Changhee polynomials are established.