Generalized double Fibonomial numbers

Abstract

From the beginning of 20th century, generalization of binomial coefficient has been deliberated broadly. One of the most famous generalized binomial coefficients are Fibonomial coefficients, obtained by substituting Fibonacci numbers in place of natural numbers in the binomial coefficients. In this paper, we further generalize the concept of Fibonomial coefficient and called it Generalized double Fibonomial number and obtain interesting properties of it. We also discuss its special case, double Fibonomial number along with the situation in which they give integer values. Other properties of it have also been discussed along with its upper and lower bounds.