
    Determine the number of distinct ways to arrange n hourly emergency room staffing slots such that exactly m time periods show an increase in required staff compared to the previous hour, helping optimize personnel allocation during peak activity periods. The solution will help hospital administrators better predict and plan for varying patient volumes while maintaining optimal care delivery.
    

    
def eulerian_num(n, m):
    """
    Determine the number of distinct ways to arrange n hourly emergency room staffing slots such that exactly m time periods show an increase in required staff compared to the previous hour, helping optimize personnel allocation during peak activity periods. The solution will help hospital administrators better predict and plan for varying patient volumes while maintaining optimal care delivery.
    

    """
def eulerian_num(n, m):
    """
    Determine the number of distinct ways to arrange n hourly emergency room staffing slots such that exactly m time periods show an increase in required staff compared to the previous hour, helping optimize personnel allocation during peak activity periods. The solution will help hospital administrators better predict and plan for varying patient volumes while maintaining optimal care delivery.
    

    """
    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)