Combinatorial Formulas for Certain Sequences of Multiple Numbers

TL;DR

This paper derives combinatorial formulas for multiple analogues of classical combinatorial numbers using well poised Macdonald functions, advancing the understanding of their fundamental properties and interrelations.

Contribution

It introduces explicit combinatorial formulas for multiple binomial coefficients, Catalan, Lah numbers, and related functions in terms of well poised Macdonald functions.

Findings

Derived combinatorial formulas for multiple binomial coefficients

Established properties of multiple Catalan and Lah numbers

Connected multiple numbers with well poised Macdonald functions

Abstract

Multiple analogues of certain families of combinatorial numbers are recently constructed by the author in terms of well poised Macdonald functions, and some of their fundamental properties are developed. In this paper, we present combinatorial formulas for the well poised Macdonald functions, the multiple binomial coefficients, the multiple bracket function, and the multiple Catalan and Lah numbers.