On a family of polynomials related to $ζ(2,1)=ζ(3)$

Abstract: We give a new proof of the identity $\zeta({2,1}^l)=\zeta({3}^l)$ of the multiple zeta values, where $l=1,2,\dots$, using generating functions of the underlying generalized polylogarithms. In the course of study we arrive at (hypergeometric) polynomials satisfying 3-term recurrence relations, whose properties we examine and compare with analogous ones of polynomials originated from an (ex-)conjectural identity of Borwein, Bradley and Broadhurst.