Several combinatorial identities derived from series expansions of powers of arcsine

TL;DR

This paper derives new combinatorial identities involving ratios of binomial coefficients and Catalan numbers using series expansions of powers of the arcsine function.

Contribution

It introduces novel combinatorial identities based on series expansions of arcsine powers, connecting them to binomial coefficients and Catalan numbers.

Findings

New combinatorial identities involving binomial coefficients

Connections established between arcsine series and Catalan numbers

Potential applications in combinatorial number theory

Abstract

In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the Catalan numbers in combinatorial number theory.