
    In a city's delivery network system, determine how many different ways a fleet of delivery vehicles can be arranged such that exactly m delivery routes will have a higher efficiency rating than their subsequent routes, given n total possible routes in the network. This calculation is crucial for optimizing the fleet's daily delivery sequence and minimizing overall transportation costs.
    

    
def eulerian_num(n, m):
    """
    In a city's delivery network system, determine how many different ways a fleet of delivery vehicles can be arranged such that exactly m delivery routes will have a higher efficiency rating than their subsequent routes, given n total possible routes in the network. This calculation is crucial for optimizing the fleet's daily delivery sequence and minimizing overall transportation costs.
    

    """
def eulerian_num(n, m):
    """
    In a city's delivery network system, determine how many different ways a fleet of delivery vehicles can be arranged such that exactly m delivery routes will have a higher efficiency rating than their subsequent routes, given n total possible routes in the network. This calculation is crucial for optimizing the fleet's daily delivery sequence and minimizing overall transportation costs.
    

    """
    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)