






from numpy import exp, pi, sqrt







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase = 0.0 ,   __lowerCAmelCase = 1.0      )			->     int:
					return 1 / sqrt(2 * pi * sigma**2      ) * exp(-((x - mu) ** 2) / (2 * sigma**2)      )


if __name__ == "__main__":
	import doctest

	doctest.testmod()







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     int:
     assert isinstance(__lowerCAmelCase ,   __lowerCAmelCase      ), f'The input value of [n={number}] is not an integer'

     if number == 1:
          return 2
     elif number < 1:
          UpperCamelCase__      :       List[Any]	    =  f'The input value of [n={number}] has to be > 0'
          raise ValueError(__lowerCAmelCase      )
     else:
          UpperCamelCase__      :       Optional[Any]	    =  sylvester(number - 1      )
          UpperCamelCase__      :       str	    =  num - 1
          UpperCamelCase__      :       int	    =  num
          return lower * upper + 1


if __name__ == "__main__":
 print(F"""The 8th number in Sylvester's sequence: {sylvester(8)}""")