Conjecture on the limiting lower bound for Wecken-map density

For each $n$, let $d_n^*$ be the explicit lower-bound quantity defined by

$$d_n^*= \sum_{c=0}^{n} \sum_{b=0}^{n-c} \binom{n}{c}\binom{n-c}{b}2^b\left(\frac{n-1}{n(2n-1)^2}\right)^c K\prod_{j=1}^{b}\frac{2(n-1)^2-(2c+b+j-1)}{n(2n-1)^2},$$

where

$$K=\prod_{k=c+b+1}^{n}\frac{4(n-1)^4-(8k-6)(n-1)^2+4k^2-6k+2}{n(n-1)(2n-1)^2}.$$

Limiting lower-bound conjecture. The sequence of lower bounds satisfies

$$\lim_{n\to\infty}d_n^*=e^{-2}\approx.1353.$$

The displayed values appear to approach a limit, but the source says that the formula is too complicated to evaluate asymptotically easily. Since $d_n^*$ is a lower bound for the density of the relevant set of maps, this would identify the limiting value of this particular bound, not directly the density itself.