
    In a hospital's patient readmission risk assessment system, develop an algorithm to calculate the number of different ways that n distinct risk factors can be arranged such that exactly m risk factors have a higher severity than their subsequent factors in the sequence, which helps determine the statistical likelihood of patient readmission. The arrangement pattern of risk factors and their relative severity relationships are crucial for accurate risk stratification in the hospital's predictive model.
    

    
def eulerian_num(n, m):
    """
    In a hospital's patient readmission risk assessment system, develop an algorithm to calculate the number of different ways that n distinct risk factors can be arranged such that exactly m risk factors have a higher severity than their subsequent factors in the sequence, which helps determine the statistical likelihood of patient readmission. The arrangement pattern of risk factors and their relative severity relationships are crucial for accurate risk stratification in the hospital's predictive model.
    

    """
def eulerian_num(n, m):
    """
    In a hospital's patient readmission risk assessment system, develop an algorithm to calculate the number of different ways that n distinct risk factors can be arranged such that exactly m risk factors have a higher severity than their subsequent factors in the sequence, which helps determine the statistical likelihood of patient readmission. The arrangement pattern of risk factors and their relative severity relationships are crucial for accurate risk stratification in the hospital's predictive 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)