



"""simple docstring"""
def      __magic_name__				(							lowercase = 100 ):
   SCREAMING_SNAKE_CASE_: Any     			=0
   SCREAMING_SNAKE_CASE_: str     			=0
   for i in range(1							,			n + 1 ):
      sum_of_squares += i**2
      sum_of_ints += i
   return sum_of_ints**2 - sum_of_squares


if __name__ == "__main__":
   print(f"""{solution() = }""")








"""simple docstring"""
def      __magic_name__				(							lowercase ):
   if upper_limit < 0:
      raise ValueError("""Limit for the Catalan sequence must be ≥ 0""" )

   SCREAMING_SNAKE_CASE_: Tuple     			=[0] * (upper_limit + 1)

   # Base case: C(0) = C(1) = 1
   SCREAMING_SNAKE_CASE_: Any     			=1
   if upper_limit > 0:
      SCREAMING_SNAKE_CASE_: List[str]     			=1

   # Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
   for i in range(2							,			upper_limit + 1 ):
      for j in range(lowercase ):
         catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

   return catalan_list


if __name__ == "__main__":
   print("""\n********* Catalan Numbers Using Dynamic Programming ************\n""")
   print("""\n*** Enter -1 at any time to quit ***""")
   print("""\nEnter the upper limit (≥ 0) for the Catalan number sequence: """, end="""""")
   try:
      while True:
         _UpperCAmelCase     =			int(input().strip())
         if N < 0:
            print("""\n********* Goodbye!! ************""")
            break
         else:
            print(f"""The Catalan numbers from 0 through {N} are:""")
            print(catalan_numbers(N))
            print("""Try another upper limit for the sequence: """, end="""""")
   except (NameError, ValueError):
      print("""\n********* Invalid input, goodbye! ************\n""")

   import doctest

   doctest.testmod()



