
    In a hospital's capacity management system, determine the number of ways to arrange n available beds where exactly m beds appear in a sequence such that each bed's occupancy status is greater than its previous bed's status. This calculation is crucial for optimizing bed allocation and predicting admission patterns across different hospital departments.
    

    
def eulerian_num(n, m):
    """
    In a hospital's capacity management system, determine the number of ways to arrange n available beds where exactly m beds appear in a sequence such that each bed's occupancy status is greater than its previous bed's status. This calculation is crucial for optimizing bed allocation and predicting admission patterns across different hospital departments.
    

    """
def eulerian_num(n, m):
    """
    In a hospital's capacity management system, determine the number of ways to arrange n available beds where exactly m beds appear in a sequence such that each bed's occupancy status is greater than its previous bed's status. This calculation is crucial for optimizing bed allocation and predicting admission patterns across different hospital departments.
    

    """
    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)