
    Design a function for the loan approval system that calculates the number of possible ways to prioritize n credit assessment factors such that exactly m factors receive a higher importance rating than their subsequent factors in the evaluation sequence. The calculation must account for all possible permutations of credit factor arrangements while maintaining their relative importance in the final loan decision.
    

    
def eulerian_num(n, m):
    """
    Design a function for the loan approval system that calculates the number of possible ways to prioritize n credit assessment factors such that exactly m factors receive a higher importance rating than their subsequent factors in the evaluation sequence. The calculation must account for all possible permutations of credit factor arrangements while maintaining their relative importance in the final loan decision.
    

    """
def eulerian_num(n, m):
    """
    Design a function for the loan approval system that calculates the number of possible ways to prioritize n credit assessment factors such that exactly m factors receive a higher importance rating than their subsequent factors in the evaluation sequence. The calculation must account for all possible permutations of credit factor arrangements while maintaining their relative importance in the final loan decision.
    

    """
    if m >= n or n == 0:
        return 0
    if m == 0:
        return 1
    return (n - m) * eulerian_num(n - 1, m - 1) + (m + 1) * eulerian_num(n - 1, m)