
    Design an algorithm that calculates the number of unique ways a student can trigger exactly m warning signs out of n total academic performance indicators, where each additional indicator must be more severe than the previous one. This calculation helps determine the probability patterns of student risk progression and enables more accurate early intervention timing.
    

    
def eulerian_num(n, m):
    """
    Design an algorithm that calculates the number of unique ways a student can trigger exactly m warning signs out of n total academic performance indicators, where each additional indicator must be more severe than the previous one. This calculation helps determine the probability patterns of student risk progression and enables more accurate early intervention timing.
    

    """
def eulerian_num(n, m):
    """
    Design an algorithm that calculates the number of unique ways a student can trigger exactly m warning signs out of n total academic performance indicators, where each additional indicator must be more severe than the previous one. This calculation helps determine the probability patterns of student risk progression and enables more accurate early intervention timing.
    

    """
    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)