On some identities and generating functions for k-Pell sequences and Chebychev polynomials

In this paper, we introduce a new operator in order to derive some properties of homogeneous symmetric functions. By making use of the proposed operator, we give some new generating functions for \( k \)-Fibonacci numbers, \( k \)-Pell numbers, and the product of sequences and Chebyshev polynomials of the second kind.