
    Design an algorithm for an adaptive learning system that calculates the number of distinct ways a student can progress through n difficulty levels while experiencing exactly m increases in challenge level during their learning journey. The system needs this calculation to optimize the learning path and ensure appropriate content progression based on student performance.
    

    
def eulerian_num(n, m):
    """
    Design an algorithm for an adaptive learning system that calculates the number of distinct ways a student can progress through n difficulty levels while experiencing exactly m increases in challenge level during their learning journey. The system needs this calculation to optimize the learning path and ensure appropriate content progression based on student performance.
    

    """
def eulerian_num(n, m):
    """
    Design an algorithm for an adaptive learning system that calculates the number of distinct ways a student can progress through n difficulty levels while experiencing exactly m increases in challenge level during their learning journey. The system needs this calculation to optimize the learning path and ensure appropriate content progression based on student performance.
    

    """
    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)