
    Given a patient's total number of tracked medical conditions (n) and a critical threshold of adverse events (m), develop an algorithm to calculate the number of possible ways these medical conditions can be arranged where exactly m conditions show increased severity compared to their subsequent conditions, which is essential for predicting hospital readmission risk. The result should follow the Eulerian number pattern a(n,m) where n represents the total conditions and m represents the threshold of severity increases, helping healthcare providers assess readmission probability patterns.
    

    
def eulerian_num(n, m):
    """
    Given a patient's total number of tracked medical conditions (n) and a critical threshold of adverse events (m), develop an algorithm to calculate the number of possible ways these medical conditions can be arranged where exactly m conditions show increased severity compared to their subsequent conditions, which is essential for predicting hospital readmission risk. The result should follow the Eulerian number pattern a(n,m) where n represents the total conditions and m represents the threshold of severity increases, helping healthcare providers assess readmission probability patterns.
    

    """
def eulerian_num(n, m):
    """
    Given a patient's total number of tracked medical conditions (n) and a critical threshold of adverse events (m), develop an algorithm to calculate the number of possible ways these medical conditions can be arranged where exactly m conditions show increased severity compared to their subsequent conditions, which is essential for predicting hospital readmission risk. The result should follow the Eulerian number pattern a(n,m) where n represents the total conditions and m represents the threshold of severity increases, helping healthcare providers assess readmission probability patterns.
    

    """
    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)