
    Design an algorithm for the content recommendation engine that calculates the number of distinct ways users can generate n sequential social media interactions where exactly m interactions have higher engagement than their following interaction. This pattern analysis helps determine optimal content scheduling and user engagement predictions within the recommendation system.
    

    
def eulerian_num(n, m):
    """
    Design an algorithm for the content recommendation engine that calculates the number of distinct ways users can generate n sequential social media interactions where exactly m interactions have higher engagement than their following interaction. This pattern analysis helps determine optimal content scheduling and user engagement predictions within the recommendation system.
    

    """
def eulerian_num(n, m):
    """
    Design an algorithm for the content recommendation engine that calculates the number of distinct ways users can generate n sequential social media interactions where exactly m interactions have higher engagement than their following interaction. This pattern analysis helps determine optimal content scheduling and user engagement predictions within the recommendation system.
    

    """
    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)