
    Design a fraud detection algorithm that calculates how many ways n distinct transaction patterns can be arranged such that exactly m patterns show higher risk scores than their subsequent patterns in the sequence. The result will help prioritize which transaction sequences require immediate investigation based on their relative risk positioning.
    

    
def eulerian_num(n, m):
    """
    Design a fraud detection algorithm that calculates how many ways n distinct transaction patterns can be arranged such that exactly m patterns show higher risk scores than their subsequent patterns in the sequence. The result will help prioritize which transaction sequences require immediate investigation based on their relative risk positioning.
    

    """
def eulerian_num(n, m):
    """
    Design a fraud detection algorithm that calculates how many ways n distinct transaction patterns can be arranged such that exactly m patterns show higher risk scores than their subsequent patterns in the sequence. The result will help prioritize which transaction sequences require immediate investigation based on their relative risk positioning.
    

    """
    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)