
    Given a student essay with n paragraphs and m effective transitions between them, determine the number of possible ways to arrange the paragraphs such that exactly m paragraphs have stronger connections to their following paragraph than to their preceding one. This arrangement metric helps evaluate the essay's overall flow and structural coherence.
    

    
def eulerian_num(n, m):
    """
    Given a student essay with n paragraphs and m effective transitions between them, determine the number of possible ways to arrange the paragraphs such that exactly m paragraphs have stronger connections to their following paragraph than to their preceding one. This arrangement metric helps evaluate the essay's overall flow and structural coherence.
    

    """
def eulerian_num(n, m):
    """
    Given a student essay with n paragraphs and m effective transitions between them, determine the number of possible ways to arrange the paragraphs such that exactly m paragraphs have stronger connections to their following paragraph than to their preceding one. This arrangement metric helps evaluate the essay's overall flow and structural coherence.
    

    """
    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)