On Some Identities And Generating Function of Both K-jacobsthal Numbers and Symmetric Functions in Several Variables

Abstract

In this paper, we derive new generating functions for the products of $k$-Fibonacci numbers at negative indices, $k$-Pell numbers at negative indices, $k$-Jacobsthal numbers at negative indices, the\ product of $k$-Fibonacci numbers and Tribonacci numbers, Jacobsthal polynomials and symmetric functions in several variables by making use of useful properties of the symmetric functions.