code: def betabin_like(x, alpha, beta, n):
      R
      return flib.betabin_like(x, alpha, beta, n)
docs: R"""
      Beta-binomial log-likelihood. Equivalent to binomial random
      variables with probabilities drawn from a
      :math:`\texttt{Beta}(\alpha,\beta)` distribution.
  
      .. math::
          f(x \mid \alpha, \beta, n) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)} \frac{\Gamma(n+1)}{\Gamma(x+1)\Gamma(n-x+1)} \frac{\Gamma(\alpha + x)\Gamma(n+\beta-x)}{\Gamma(\alpha+\beta+n)}
  
      :Parameters:
        - `x` : x=0,1,\ldots,n
        - `alpha` : alpha > 0
        - `beta` : beta > 0
        - `n` : n=x,x+1,\ldots
  
      :Example:
        >>> betabin_like(3,1,1,10)
        -2.3978952727989
  
      .. note::
        - :math:`E(X)=n\frac{\alpha}{\alpha+\beta}`
        - :math:`Var(X)=n\frac{\alpha \beta}{(\alpha+\beta)^2(\alpha+\beta+1)}`