
    In a healthcare monitoring system tracking elderly patient safety, develop an algorithm to calculate the number of distinct ways a patient's daily sequence of movement patterns can be arranged such that exactly m transitions between activities are greater than their subsequent transitions, given n total monitored activities. This calculation helps identify potential fall-risk patterns in the patient's daily movement sequences, enabling proactive fall prevention measures.
    

    
def eulerian_num(n, m):
    """
    In a healthcare monitoring system tracking elderly patient safety, develop an algorithm to calculate the number of distinct ways a patient's daily sequence of movement patterns can be arranged such that exactly m transitions between activities are greater than their subsequent transitions, given n total monitored activities. This calculation helps identify potential fall-risk patterns in the patient's daily movement sequences, enabling proactive fall prevention measures.
    

    """
def eulerian_num(n, m):
    """
    In a healthcare monitoring system tracking elderly patient safety, develop an algorithm to calculate the number of distinct ways a patient's daily sequence of movement patterns can be arranged such that exactly m transitions between activities are greater than their subsequent transitions, given n total monitored activities. This calculation helps identify potential fall-risk patterns in the patient's daily movement sequences, enabling proactive fall prevention measures.
    

    """
    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)