code: def binomial_coefficients(n):
      """Return a dictionary containing pairs :math:`{(k1,k2) : C_kn}` where
      :math:`C_kn` are binomial coefficients and :math:`n=k1+k2`.
  
      Examples
      ========
  
      >>> from sympy.ntheory import binomial_coefficients
      >>> binomial_coefficients(9)
      {(0, 9): 1, (1, 8): 9, (2, 7): 36, (3, 6): 84,
       (4, 5): 126, (5, 4): 126, (6, 3): 84, (7, 2): 36, (8, 1): 9, (9, 0): 1}
  
      See Also
      ========
  
      binomial_coefficients_list, multinomial_coefficients
      """
      n = as_int(n)
      d = {(0, n): 1, (n, 0): 1}
      a = 1
      for k in range(1, n // 2 + 1):
          a = (a * (n - k + 1)) // k
          d[k, n - k] = d[n - k, k] = a
      return d
  
imports: from sympy.utilities.misc import as_int
label_desc: Use image node_id 1 for calling a global function with example usage: binomial_coefficients(n) and returns: d