
    Given n different patient categories in the emergency room, determine the number of possible ways to organize these categories into separate treatment groups, where each category must be assigned to exactly one group and empty groups are allowed. Each distinct arrangement of patient categories represents a unique resource allocation strategy that could help optimize emergency room operations and minimize wait times.
    

    
def bell_number(n):
    """
    Given n different patient categories in the emergency room, determine the number of possible ways to organize these categories into separate treatment groups, where each category must be assigned to exactly one group and empty groups are allowed. Each distinct arrangement of patient categories represents a unique resource allocation strategy that could help optimize emergency room operations and minimize wait times.
    

    """
def bell_number(n):
    """
    Given n different patient categories in the emergency room, determine the number of possible ways to organize these categories into separate treatment groups, where each category must be assigned to exactly one group and empty groups are allowed. Each distinct arrangement of patient categories represents a unique resource allocation strategy that could help optimize emergency room operations and minimize wait times.
    

    """
    bell = [[0 for i in range(n + 1)] for j in range(n + 1)]
    bell[0][0] = 1
    for i in range(1, n + 1):
        bell[i][0] = bell[i - 1][i - 1]
        for j in range(1, i + 1):
            bell[i][j] = bell[i - 1][j - 1] + bell[i][j - 1]
    return bell[n][0]