On some binomial coefficients related to the evaluation of tan(nx)

TL;DR

This paper investigates specific binomial coefficients linked to calculating tan(nx), revealing their connection to derivative polynomials for tangent and secant functions.

Contribution

It introduces a novel relationship between binomial coefficients and derivative polynomials for tangent and secant, enhancing understanding of their combinatorial properties.

Findings

Established a connection between binomial coefficients and derivative polynomials.

Provided formulas relating binomial coefficients to tangent and secant derivatives.

Enhanced mathematical tools for evaluating tan(nx) using combinatorial methods.

Abstract

The purpose of this paper is to study some binomial coefficients which are related to the evaluation of tan(nx). We present a connection between these binomial coefficients and the coefficients of a family of derivative polynomials for tangent and secant.