
    Design an algorithm for an adaptive learning system that calculates the number of different ways a student can progress through n difficulty levels while experiencing exactly m increases in challenge level during their learning journey. The system needs to track when the current lesson is more challenging than the previous one, counting it as an "increase" in the learning curve, to help optimize the student's learning path.
    

    
def eulerian_num(n, m):
    """
    Design an algorithm for an adaptive learning system that calculates the number of different ways a student can progress through n difficulty levels while experiencing exactly m increases in challenge level during their learning journey. The system needs to track when the current lesson is more challenging than the previous one, counting it as an "increase" in the learning curve, to help optimize the student's learning path.
    

    """
def eulerian_num(n, m):
    """
    Design an algorithm for an adaptive learning system that calculates the number of different ways a student can progress through n difficulty levels while experiencing exactly m increases in challenge level during their learning journey. The system needs to track when the current lesson is more challenging than the previous one, counting it as an "increase" in the learning curve, to help optimize the student's learning path.
    

    """
    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)