The odd periodic highest-coefficient conjecture for the loop model

Let $F_{2n+1}(x)$ be the generating polynomial associated with the odd-sized periodic ground state, let ${\rm A}_n$ denote the number of $n\times n$ alternating sign matrices, and let ${\rm AHT}_{2n+1}$ denote the corresponding sum rule. Odd periodic highest-coefficient conjecture. The conjectured asymptotic coefficient is

$$\lim_{x\to\infty}\frac{F_{2n+1}(x)}{x^n}=\frac{{\rm A}_n^2}{{\rm AHT}_{2n+1}}.$$

The source attributes this conjecture to an earlier paper and presents it among observations for the odd periodic model, for which an equivalent general formula was not known there.