International Journal of Mathematics and Mathematical Sciences 
Volume 14 (1991), Issue 2, Pages 239-244
doi:10.1155/S0161171291000261

Vieta's triangular array and a related family of polynomials

Neville Robbins

 Department of Mathematics, San Francisco State University, San Francisco 94132, CA, USA
Received 2 November 1988; Revised 12 December 1988

Abstract

If n≥1, let the nth row of an infinite triangular array consist of entries B(n,j)=nn−j(jn−j), where 0≤j≤[12n].

We develop some properties of this array, which was discovered by Vieta. In addition, we prove some irreducibility properties of the family of polynomials Vn(x)=∑j=0[12n](−1)jB(n,j)xn−2j.

These polynomials, which we call Vieta polynomials, are related to Chebychev polynomials of the first kind.