Question: 
Write a function to find n-th rencontres number.


Model's Code:
def rencontres_number(n, k):
    from math import factorial
    if k > n or k < 0:
        return 0
    return factorial(n) // (factorial(k) * factorial(n - k)) * (1 if k == 0 else 1)



Sample Correct Code:
def binomial_coeffi(n, k): 
	if (k == 0 or k == n): 
		return 1
	return (binomial_coeffi(n - 1, k - 1) 
		+ binomial_coeffi(n - 1, k)) 
def rencontres_number(n, m): 
	if (n == 0 and m == 0): 
		return 1
	if (n == 1 and m == 0): 
		return 0
	if (m == 0): 
		return ((n - 1) * (rencontres_number(n - 1, 0)+ rencontres_number(n - 2, 0))) 
	return (binomial_coeffi(n, m) * rencontres_number(n - m, 0))


Asserts:
assert rencontres_number(7, 2) == 924
assert rencontres_number(3, 0) == 2
assert rencontres_number(3, 1) == 3


Tests:
Test 1 of 3: FAIL: AssertionError()

Test 926 of 974: 710/926 (76.67386609071274%): failed