Conjectural resolution counts for Type I four-dimensional quiver varieties

Let $N(\I(\D[4],n))$, $N(\I(\D[m],1))$, $N(\I(\D[m],n)')$, $N(\I(\D[m],0)')$, $N(\I(\E[6,7],n))$, and $N(\I(m))$ denote the numbers of projective crepant resolutions for the indicated Type $\I$ dimension vectors. Type I resolution-count conjecture. For certain dimension vectors in Type $\I$, these numbers are

$$N(\I(\D[4],n))=\frac{n+3}{3}\binom{n+5}{5},$$ $$N(\I(\D[m],1))=2^{m-1},$$ $$N(\I(\D[m],n)')=\frac{2(m+n-1)}{n!}\prod_{i=1}^{n-1}(2m+i-2),\qquad N(\I(\D[m],0)')=1,$$

$N(\I(\E[6,7],n))$ coincides with the dimensions of multiples of the minimal representation of the $\E[6,7]$ complex Lie algebra, and

$$N(\I(m))=\prod_{i=0}^{m-1}\frac{(2i)!(m+2i+1)!}{(3i+1)!(m+i)!},$$

which coincides with the number of totally symmetric plane partitions fitting in an $m\times m\times m$ box. These formulas are presented as computer-aided numerology based on computed cases, and the source does not explicitly establish their conjectural status or resolution.