
    In a social networking platform, determine the number of ways to rank connection paths between two users where exactly m paths have a stronger relationship strength than their immediately following path, given n total possible connection paths through mutual friends. The ranking system helps prioritize friend recommendations by considering the relative strength of each connection path, where a stronger path should appear earlier in the recommendation list.
    

    
def eulerian_num(n, m):
    """
    In a social networking platform, determine the number of ways to rank connection paths between two users where exactly m paths have a stronger relationship strength than their immediately following path, given n total possible connection paths through mutual friends. The ranking system helps prioritize friend recommendations by considering the relative strength of each connection path, where a stronger path should appear earlier in the recommendation list.
    

    """
def eulerian_num(n, m):
    """
    In a social networking platform, determine the number of ways to rank connection paths between two users where exactly m paths have a stronger relationship strength than their immediately following path, given n total possible connection paths through mutual friends. The ranking system helps prioritize friend recommendations by considering the relative strength of each connection path, where a stronger path should appear earlier in the recommendation list.
    

    """
    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)