def METHOD_NAME(self):
    n = torch.tensor(self.total_count)
    cat_entropy = self._categorical.METHOD_NAME()
    term1 = n * cat_entropy - torch.lgamma(n + 1)
    support = self._binomial.enumerate_support(expand=False)[1:]
    binomial_probs = torch.exp(self._binomial.log_prob(support))
    weights = torch.lgamma(support + 1)
    term2 = (binomial_probs * weights).sum([0, -1])
    return term1 + term2