A note on the Borwein conjecture

Jiyou Li

A conjecture of Borwein asserts that for any positive integers $n$ and $k$, the coefficient $a_{3k}$ of $q^{3k}$ in the expansion of ${\prod }_{j=0}^n(1-q^{3j+1})(1-q^{3j+2})$ is non…