code: def num_compositions(m, n):
      
      # docs.scipy.org/doc/scipy/reference/generated/scipy.special.comb.html
      return scipy.special.comb(n+m-1, m-1, exact=True)
docs: The total number of m-part compositions of n, which is equal to
      (n+m-1) choose (m-1).
  
      Parameters
      ----------
      m : scalar(int)
          Number of parts of composition.
  
      n : scalar(int)
          Integer to decompose.
  
      Returns
      -------
      scalar(int)
          Total number of m-part compositions of n.