The First Borwein conjecture on the polynomials $A_n(q)$, $B_n(q)$ and $C_n(q)$

The polynomials $A_n(q)$, $B_n(q)$ and $C_n(q)$ are defined by

$$\prod_{k=1}^n(1-q^{3k-2})(1-q^{3k-1})=A_n(q^3)-qB_n(q^3)-q^2C_n(q^3).$$

First Borwein conjecture. The polynomials $A_n(q)$, $B_n(q)$ and $C_n(q)$ have nonnegative coefficients.

This is the observation communicated by P. Borwein to G. E. Andrews and is the motivating special case for the generalized Borwein conjecture. The source does not state whether it has been resolved.