The coefficient ratio conjecture for complete Nevanlinna–Pick kernels

Let $a_n\}$ and $b_n\}$ be sequences related as in equation (4.1), and suppose that

$$\sum_{n=1}^\infty b_n=1.$$

Coefficient ratio conjecture. Then

$$\lim_{n\to\infty}\frac{a_n}{a_{n+1}}=1.$$

This concerns the asymptotic behavior of coefficients defining a radial complete Nevanlinna–Pick kernel. The supplied text does not state whether the claim has been proved or disproved.