






def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__  )	->    Optional[int]:
  UpperCamelCase_: Optional[Any]   				=    [0 for i in range(r + 1  )]
  # nc0 = 1
  UpperCamelCase_: Union[str, Any]   				=    1
  for i in range(1     ,   n + 1  ):
    # to compute current row from previous row.
    UpperCamelCase_: Optional[Any]   				=    min(UpperCAmelCase__     ,   UpperCAmelCase__  )
    while j > 0:
      c[j] += c[j - 1]
      j -= 1
  return c[r]
print(binomial_coefficient(n=10, r=5))







def   snake_case (UpperCAmelCase__  )	->    int:
  assert isinstance(UpperCAmelCase__     ,   UpperCAmelCase__  ), 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(UpperCAmelCase__  )
  else:
    UpperCamelCase_: str   				=    sylvester(number - 1  )
    UpperCamelCase_: str   				=    num - 1
    UpperCamelCase_: Any   				=    num
    return lower * upper + 1


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