I'm trying to do the same thing that was done in this question:
Calculating the parameters of a Beta distribution using the mean and variance
for the Beta-Binomial distribution for which the mean is
$\mu = n\frac{\alpha}{\alpha+\beta}$
and the variance is
$\sigma^2 = n\frac{\alpha\beta(\alpha+\beta+n)}{(\alpha+\beta)^2(\alpha+\beta+1)}$
How can I calculate $\alpha$ and $\beta$ in terms of $\mu$ and $\sigma^2$ for a given $n$?
Also some information regarding the bound of the mean and variance similar to the answer above would be appreciated, e.g. I know that $\mu \in (0,n)$.