
    In a mobile banking app's multi-step authentication system, determine the number of different ways to arrange n available security verification methods (like fingerprint, facial recognition, and PIN) where exactly m verification steps have a higher security level than the verification step that follows them. This calculation helps establish optimal security verification sequences for different transaction values while maintaining user convenience.
    

    
def eulerian_num(n, m):
    """
    In a mobile banking app's multi-step authentication system, determine the number of different ways to arrange n available security verification methods (like fingerprint, facial recognition, and PIN) where exactly m verification steps have a higher security level than the verification step that follows them. This calculation helps establish optimal security verification sequences for different transaction values while maintaining user convenience.
    

    """
def eulerian_num(n, m):
    """
    In a mobile banking app's multi-step authentication system, determine the number of different ways to arrange n available security verification methods (like fingerprint, facial recognition, and PIN) where exactly m verification steps have a higher security level than the verification step that follows them. This calculation helps establish optimal security verification sequences for different transaction values while maintaining user convenience.
    

    """
    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)