The beta-binomial distribution has probability mass function
$$f_{BB}(x;\mu,\phi)={n\choose x} \frac{\Gamma{(\phi)}}{\Gamma{(\mu\phi)}\Gamma{((1-\mu)\phi)}} \frac{\Gamma{(\mu\phi+x)}\Gamma{((1-\mu)\phi + n - x)}}{\Gamma{(\phi + n)}},$$
for \(x \in \lbrace 0, 1, \dots, n \rbrace\), where \(0<\mu<1\) identifies the mean and \(\phi=(1-\theta)/\theta >0\) is the precision parameter.