code: def test_multinomial_coefficients():
      assert multinomial_coefficients(1, 1) == {(1,): 1}
      assert multinomial_coefficients(1, 2) == {(2,): 1}
      assert multinomial_coefficients(1, 3) == {(3,): 1}
      assert multinomial_coefficients(2, 0) == {(0, 0): 1}
      assert multinomial_coefficients(2, 1) == {(0, 1): 1, (1, 0): 1}
      assert multinomial_coefficients(2, 2) == {
          (2, 0): 1,
          (0, 2): 1,
          (1, 1): 2,
      }
      assert multinomial_coefficients(2, 3) == {
          (3, 0): 1,
          (1, 2): 3,
          (0, 3): 1,
          (2, 1): 3,
      }
      assert multinomial_coefficients(3, 1) == {
          (1, 0, 0): 1,
          (0, 1, 0): 1,
          (0, 0, 1): 1,
      }
      assert multinomial_coefficients(3, 2) == {
          (0, 1, 1): 2,
          (0, 0, 2): 1,
          (1, 1, 0): 2,
          (0, 2, 0): 1,
          (1, 0, 1): 2,
          (2, 0, 0): 1,
      }
      mc = multinomial_coefficients(3, 3)
      assert mc == {
          (2, 1, 0): 3,
          (0, 3, 0): 1,
          (1, 0, 2): 3,
          (0, 2, 1): 3,
          (0, 1, 2): 3,
          (3, 0, 0): 1,
          (2, 0, 1): 3,
          (1, 2, 0): 3,
          (1, 1, 1): 6,
          (0, 0, 3): 1,
      }
      assert dict(multinomial_coefficients_iterator(2, 0)) == {
          (0, 0): 1
      }
      assert dict(multinomial_coefficients_iterator(2, 1)) == {
          (0, 1): 1,
          (1, 0): 1,
      }
      assert dict(multinomial_coefficients_iterator(2, 2)) == {
          (2, 0): 1,
          (0, 2): 1,
          (1, 1): 2,
      }
      assert dict(multinomial_coefficients_iterator(3, 3)) == mc
      it = multinomial_coefficients_iterator(7, 2)
      assert [next(it) for i in range(4)] == [
          ((2, 0, 0, 0, 0, 0, 0), 1),
          ((1, 1, 0, 0, 0, 0, 0), 2),
          ((0, 2, 0, 0, 0, 0, 0), 1),
          ((1, 0, 1, 0, 0, 0, 0), 2),
      ]
  
imports: from sympy.ntheory.multinomial import binomial_coefficients, binomial_coefficients_list, multinomial_coefficients
  from sympy.ntheory.multinomial import multinomial_coefficients_iterator
label_desc: Use image node_id 3 for calling a global function with example usage: test_multinomial_coefficients() without return types