The asymptotic growth constant formula for Sierpinski gaskets

Let $SG_d(n)$ be the $d$-dimensional Sierpinski gasket at stage $n$, and let $z_{SG_d}$ denote its asymptotic growth constant for spanning trees. Then

Asymptotic growth constant conjecture. The asymptotic growth constant is

$$z_{SG_d}=\frac{d-1}{d(d+1)}\bigl[d\ln 2+(d+1)\ln(d+1)+\ln(d+3)\bigr].$$

This formula is presented as a consequence of the preceding spanning-tree conjecture and the known vertex-count formula for $SG_d(n)$. Its general status is not resolved in the supplied text.