
    In a credit scoring system that evaluates multiple financial factors, determine the number of ways to assign relative importance rankings to n distinct credit metrics such that exactly m factors have a higher ranking than their preceding factor in the sequence. This calculation is crucial for optimizing the weighting scheme in the bank's credit assessment model.
    

    
def eulerian_num(n, m):
    """
    In a credit scoring system that evaluates multiple financial factors, determine the number of ways to assign relative importance rankings to n distinct credit metrics such that exactly m factors have a higher ranking than their preceding factor in the sequence. This calculation is crucial for optimizing the weighting scheme in the bank's credit assessment model.
    

    """
def eulerian_num(n, m):
    """
    In a credit scoring system that evaluates multiple financial factors, determine the number of ways to assign relative importance rankings to n distinct credit metrics such that exactly m factors have a higher ranking than their preceding factor in the sequence. This calculation is crucial for optimizing the weighting scheme in the bank's credit assessment model.
    

    """
    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)