
    Develop an algorithm to calculate the number of possible ways that n patient arrival patterns in an emergency room can be arranged such that exactly m time slots show an increase in patient volume compared to the previous hour. This calculation will help predict and optimize staffing levels across different time periods in the emergency department's daily schedule.
    

    
def eulerian_num(n, m):
    """
    Develop an algorithm to calculate the number of possible ways that n patient arrival patterns in an emergency room can be arranged such that exactly m time slots show an increase in patient volume compared to the previous hour. This calculation will help predict and optimize staffing levels across different time periods in the emergency department's daily schedule.
    

    """
def eulerian_num(n, m):
    """
    Develop an algorithm to calculate the number of possible ways that n patient arrival patterns in an emergency room can be arranged such that exactly m time slots show an increase in patient volume compared to the previous hour. This calculation will help predict and optimize staffing levels across different time periods in the emergency department's daily schedule.
    

    """
    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)