An array of numbers is constructed beginning with the numbers $-1\qquad3\qquad1$ in the top row. Each adjacent pair of numbers is summed to produce a number in the next row. Each row begins and ends with $-1$ and $1$ , respectively.

$$\begin{array}{ccccccccc} &&-1&&3&&1&&\\ &-1&&2&&4&&1&\\ -1&&1&&6&&5&&1\\ \end{array}$$

If the process continues, one of the rows will sum to $12,288$ . In that row, what is the third number from the left?