Stirling's approximation for central extended binomial coefficients

TL;DR

This paper derives asymptotic formulas for central extended binomial coefficients by relating their distribution to the normal distribution via the Central Limit Theorem, extending classical binomial coefficient analysis.

Contribution

It introduces asymptotic formulas for extended binomial coefficients, generalizing classical binomial coefficient approximations using probabilistic methods.

Findings

Asymptotic formulas for central extended binomial coefficients derived

Connection established between discrete uniform sums and normal distribution

Extension of classical binomial coefficient asymptotics

Abstract

We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients. To do so, we relate the exact distribution of the sum of independent discrete uniform random variables to the asymptotic distribution, obtained from the Central Limit Theorem and a local limit variant.