N = 2:

S 1 S 1 = 1 = S 2

N = 3:

S 1 S 2 + S 2 S 1 = 1 + 1 = 2 = S 3

N = 4:

S 1 S 3 + S 2 S 2 + S 3 S 1 = 2 + 1 + 2 = 5 = S 4

N = 5:

S 1 S 4 + S 2 S 3 + S 3 S 2 + S 4 S 1 = 5 + 2 + 2 + 5 = 14 = S 5

N = 6:

S 1 S 5 + S 2 S 4 + S 3 S 3 + S 4 S 2 + S 5 S 1 = 14 + 5 + 4 + 5 + 14 = 42 = S 6

N = 7:

S 1 S 6 + S 2 S 5 + S 3 S 4 + S 4 S 3 + S 5 S 2 + S 6 S 1 = 42 + 14 + 10 + 10 + 14 + 42 = 132 = S 7

N = 8:

S 1 S 7 + S 2 S 6 + S 3 S 5 + S 4 S 4 + S 5 S 3 + S 6 S 2 + S 1 S 1 = 2 × ( 132 + 42 + 28 ) + 25 = 429 = S 8

N = 9:

S 1 S 8 + S 2 S 7 + S 3 S 6 + S 4 S 5 + S 5 S 4 + S 6 S 3 + S 7 S 2 + S 8 S 1 = 2 × ( 429 + 132 + 84 + 70 ) = 2 × 715 = 1430 = S 9

N = 10:

S 1 S 9 + S 2 S 8 + S 3 S 7 + S 4 S 6 + S 5 S 5 + S 6 S 4 + S 7 S 3 + S 8 S 2 + S 9 S 1 = 2 × ( 1430 + 429 + 264 + 210 ) + 196 = 4862 = S 10