
    Design a fraud detection algorithm that determines how many different ways n consecutive transactions can be arranged such that exactly m transactions have a higher value than their following transaction, which helps identify suspicious spending patterns. The algorithm must analyze the relative ordering of transaction amounts within a specified time window to detect potential fraudulent sequences.
    

    
def eulerian_num(n, m):
    """
    Design a fraud detection algorithm that determines how many different ways n consecutive transactions can be arranged such that exactly m transactions have a higher value than their following transaction, which helps identify suspicious spending patterns. The algorithm must analyze the relative ordering of transaction amounts within a specified time window to detect potential fraudulent sequences.
    

    """
def eulerian_num(n, m):
    """
    Design a fraud detection algorithm that determines how many different ways n consecutive transactions can be arranged such that exactly m transactions have a higher value than their following transaction, which helps identify suspicious spending patterns. The algorithm must analyze the relative ordering of transaction amounts within a specified time window to detect potential fraudulent sequences.
    

    """
    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)