1^2 + 1^2 = 2 = 2 *C(1,1)
1^2 + 2^2 + 1^2 = 6 = 2 *C(3, 2)
1^2 + 3^2 + 3^2 + 1^2 = 20 = 2*C ( 5, 3)
1^2 + 4^2 + 6^2 + 4^2 + 1^2 = 70 = 2 * C (7,4)
1^2 + 5^2 + 10^2 + 10^2 + 5^2 + 1^2 = 252 = 2 * C ( 9, 5)
The sum of the squares of the nth row entries in Pascal's Triangle seems to be :
2 * C ( 2n - 1 , n)
Note that these successive sums appear as the "middle" term in row 2n of the triangle......!!!!