1, 2, 3, 4, 5, 6, 7   ai = i

1, 3, 5, 7, 9, 11, 13  ai = 2i-1

1, 4, 9, 16, 25, 36, 49  ai = i**2

2, 6, 12, 20, 30, 42, 56  ai = i*(i+1)

2, 4, 8, 16, 32, 64, 128  ai = 2**i

2, 5, 8, 11, 14  ai = 3 * i - 1

2, 5, 10, 17, 26  ai = i**2 + 1

1/2, 2/3, 3/4, 4/5, 5/6  ai = i / (i + 1)

1/2, 3/4, 5/6, 7/8, 9/10  ai = (2*i - 1) / (2*i)

1/1, 2/3, 3/5, 4/7, 5/9  ai = i / (2*i - 1)

1, 2, 6, 24, 120, 720, 5040  ai = factorial(i)  from math import factorial