Test.py

def factorial(n):
    if (n == 0):
        return 1
    elif (n == 1):
        return n
    else:
        return n * factorial(n-1)
        
def nCk(n,k): 
  return factorial(n)/(factorial(k)*factorial(n-k))


def noCouples(n):
    total = 0
    for k in range(0,n+1):
        total += nCk(n,k) * 2**k * factorial(2*n-k) * (-1)**(k)
    return total


print noCouples(4)