
    Design an algorithm that calculates the number of possible personalized learning sequences where a student can progress through n learning modules while making exactly m transitions between difficulty levels (where a transition occurs when moving from an easier module to a more challenging one). The sequence must ensure continuous learning progress while accommodating the student's need to adjust difficulty levels based on their learning style and mastery.
    

    
def eulerian_num(n, m):
    """
    Design an algorithm that calculates the number of possible personalized learning sequences where a student can progress through n learning modules while making exactly m transitions between difficulty levels (where a transition occurs when moving from an easier module to a more challenging one). The sequence must ensure continuous learning progress while accommodating the student's need to adjust difficulty levels based on their learning style and mastery.
    

    """
def eulerian_num(n, m):
    """
    Design an algorithm that calculates the number of possible personalized learning sequences where a student can progress through n learning modules while making exactly m transitions between difficulty levels (where a transition occurs when moving from an easier module to a more challenging one). The sequence must ensure continuous learning progress while accommodating the student's need to adjust difficulty levels based on their learning style and mastery.
    

    """
    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)