Wieland-type chord-diagram identity for fully packed loops

Let $i,j,\ell,m\geq 0$, and let $A_X$ denote the number associated with a link pattern $X$ in the paper's chord-diagram notation. Wieland-type chord-diagram conjecture. The equality displayed in the source holds:

$$\text{the left-hand fully packed loop quantity}=\text{the sum represented on the right over }C_{i+j+1}\text{ chord diagrams}.$$

This is the fully packed loop relation obtained from the preceding special-values conjecture. Because the displayed diagram is not available in the supplied text, the exact quantities and their dependence on $i,j,\ell,m$ cannot be reconstructed here.