
    Design an algorithm for a patient monitoring system that calculates the number of possible ways n distinct vital sign patterns can be arranged such that exactly m patterns show an increasing trend compared to their preceding measurements. This calculation helps identify critical sequences in patient monitoring data that could indicate potential health complications.
    

    
def eulerian_num(n, m):
    """
    Design an algorithm for a patient monitoring system that calculates the number of possible ways n distinct vital sign patterns can be arranged such that exactly m patterns show an increasing trend compared to their preceding measurements. This calculation helps identify critical sequences in patient monitoring data that could indicate potential health complications.
    

    """
def eulerian_num(n, m):
    """
    Design an algorithm for a patient monitoring system that calculates the number of possible ways n distinct vital sign patterns can be arranged such that exactly m patterns show an increasing trend compared to their preceding measurements. This calculation helps identify critical sequences in patient monitoring data that could indicate potential health complications.
    

    """
    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)