code: def get_one_over_n_factorial(counter_entry):
      r
      # compute all factorials
      factos = [sp.factorial(c) for c in counter_entry]
      # multiply them
      prod = product(factos)
      # return the invert
      return sp.Integer(1)/sp.S(prod)
docs: r"""
      Calculates  the :math:`\frac{1}{\mathbf{n!}}` of eq. 6 (see Ale et al. 2013).
      That is the invert of a product of factorials.
      :param counter_entry: an entry of counter. That is an array of integers of length equal to the number of variables.
      For instance, `counter_entry` could be `[1,0,1]` for three variables.
      :return: a scalar as a sympy expression