
    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 instances where their performance improves compared to the previous level. The system needs this calculation to dynamically adjust content difficulty and ensure optimal learning paths for students based on their performance patterns.
    

    
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 instances where their performance improves compared to the previous level. The system needs this calculation to dynamically adjust content difficulty and ensure optimal learning paths for students based on their performance patterns.
    

    """
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 instances where their performance improves compared to the previous level. The system needs this calculation to dynamically adjust content difficulty and ensure optimal learning paths for students based on their performance patterns.
    

    """
    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)