
    Design an algorithm to calculate the number of distinct ways a student can progress through n learning modules while experiencing exactly m difficulty level increases, where a difficulty increase occurs when a later module is more challenging than an earlier one. This calculation helps determine the possible learning paths available to students while maintaining an optimal progression of difficulty.
    

    
def eulerian_num(n, m):
    """
    Design an algorithm to calculate the number of distinct ways a student can progress through n learning modules while experiencing exactly m difficulty level increases, where a difficulty increase occurs when a later module is more challenging than an earlier one. This calculation helps determine the possible learning paths available to students while maintaining an optimal progression of difficulty.
    

    """
def eulerian_num(n, m):
    """
    Design an algorithm to calculate the number of distinct ways a student can progress through n learning modules while experiencing exactly m difficulty level increases, where a difficulty increase occurs when a later module is more challenging than an earlier one. This calculation helps determine the possible learning paths available to students while maintaining an optimal progression of difficulty.
    

    """
    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)