
    Design an algorithm for an adaptive learning system that calculates the number of unique ways to arrange n difficulty levels such that exactly m levels are greater than the previous level in the sequence. This calculation helps determine optimal difficulty progressions for student assignments while ensuring pedagogically sound transitions between complexity levels.
    

    
def eulerian_num(n, m):
    """
    Design an algorithm for an adaptive learning system that calculates the number of unique ways to arrange n difficulty levels such that exactly m levels are greater than the previous level in the sequence. This calculation helps determine optimal difficulty progressions for student assignments while ensuring pedagogically sound transitions between complexity levels.
    

    """
def eulerian_num(n, m):
    """
    Design an algorithm for an adaptive learning system that calculates the number of unique ways to arrange n difficulty levels such that exactly m levels are greater than the previous level in the sequence. This calculation helps determine optimal difficulty progressions for student assignments while ensuring pedagogically sound transitions between complexity levels.
    

    """
    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)