The proposed Macdonald index formula for the $(A_1,D_3)$ theory

Let $(q;q)_m=\prod_{j=1}^{m}(1-q^j)$ and let $\binom{2m}{k}_q$ be the $q$-binomial coefficient. The $(A_1,D_3)$ Macdonald-index conjecture. The Macdonald index of the Argyres–Douglas theory is

$${{\cal I}}_{\mathsf{M}}^{(A_1,D_3)}(q,t)=\sum_{m=0}^{\infty}\frac{t^m}{(q;q)_m}\sum_{k=0}^{2m}\binom{2m}{k}_q.$$

The formula is motivated by matching the first columns and orders of the index with the projected free-hypermultiplet contribution; the source gives no proof or resolution.