
    Design an algorithm to calculate the number of distinct ways a student can progress through n learning modules while experiencing exactly m increases in difficulty level between consecutive modules, where a difficulty increase occurs when a later module is more challenging than its predecessor. The algorithm should help educational platforms optimize the sequencing of learning content by understanding all possible progression patterns that maintain exactly m difficulty transitions across n modules.
    

    
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 increases in difficulty level between consecutive modules, where a difficulty increase occurs when a later module is more challenging than its predecessor. The algorithm should help educational platforms optimize the sequencing of learning content by understanding all possible progression patterns that maintain exactly m difficulty transitions across n modules.
    

    """
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 increases in difficulty level between consecutive modules, where a difficulty increase occurs when a later module is more challenging than its predecessor. The algorithm should help educational platforms optimize the sequencing of learning content by understanding all possible progression patterns that maintain exactly m difficulty transitions across n modules.
    

    """
    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)