
    In a hospital's readmission risk prediction system, develop an algorithm that calculates the number of possible ways n distinct medical risk factors can be arranged such that exactly m of them have a higher severity score than the following risk factor. This calculation is crucial for weighting different combinations of risk factors in the hospital's patient readmission prediction model.
    

    
def eulerian_num(n, m):
    """
    In a hospital's readmission risk prediction system, develop an algorithm that calculates the number of possible ways n distinct medical risk factors can be arranged such that exactly m of them have a higher severity score than the following risk factor. This calculation is crucial for weighting different combinations of risk factors in the hospital's patient readmission prediction model.
    

    """
def eulerian_num(n, m):
    """
    In a hospital's readmission risk prediction system, develop an algorithm that calculates the number of possible ways n distinct medical risk factors can be arranged such that exactly m of them have a higher severity score than the following risk factor. This calculation is crucial for weighting different combinations of risk factors in the hospital's patient readmission prediction 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)