code: def contracted_norm(l, alpha, a):
      r"""Compute the normalization constant for a contracted Gaussian function.
  
      A contracted Gaussian function is defined as
  
      .. math::
  
          \psi = a_1 G_1 + a_2 G_2 + a_3 G_3,
  
      where :math:`a` denotes the contraction coefficients and :math:`G` is a primitive Gaussian function. The
      normalization constant for this function is computed as
  
      .. math::
  
          N(l, \alpha, a) = [\frac{\pi^{3/2}(2l_x-1)!! (2l_y-1)!! (2l_z-1)!!}{2^{l_x + l_y + l_z}}
          \sum_{i,j} \frac{a_i a_j}{(\alpha_i + \alpha_j)^{{l_x + l_y + l_z+3/2}}}]^{-1/2}
  
      where :math:`l` and :math:`\alpha` denote the angular momentum quantum number and the exponent
      of the Gaussian function, respectively.
  
      Args:
          l (tuple[int]): angular momentum quantum number of the primitive Gaussian functions
          alpha (array[float]): exponents of the primitive Gaussian functions
          a (array[float]): coefficients of the contracted Gaussian functions
  
      Returns:
          array[float]: normalization coefficient
  
      **Example**
  
      >>> l = (0, 0, 0)
      >>> alpha = np.array([3.425250914, 0.6239137298, 0.168855404])
      >>> a = np.array([1.79444183, 0.50032649, 0.18773546])
      >>> n = contracted_norm(l, alpha, a)
      >>> print(n)
      0.39969026908800853
      """
      lx, ly, lz = l
  
      c = (
          np.pi**1.5
          / 2 ** sum(l)
          * _fac2(2 * lx - 1)
          * _fac2(2 * ly - 1)
          * _fac2(2 * lz - 1)
      )
      s = (
          (a.reshape(len(a), 1) * a)
          / ((alpha.reshape(len(alpha), 1) + alpha) ** (sum(l) + 1.5))
      ).sum()
      n = 1 / qml.math.sqrt(c * s)
      return n
  
imports: import itertools
  import numpy
  from scipy.special import factorial2
  import pennylane
label_desc: Use image node_id 2 for calling a global function with example usage: contracted_norm(l, alpha, a) and returns: n