9. (10 points) Fill in the numbers 1-16 in a $4 \times 4$ table, such that each number in the same row to the right is greater than the one to the left; and each number in the same column below is greater than the one above. The numbers 4 and 13 are already filled in, and the remaining 14 integers can be filled in $\qquad$ different ways.
【Solution】Solution: The four cells in the upper left corner and the four cells in the lower right corner each have two ways to fill, the remaining four cells in the lower left corner and the upper right corner, there are still 8 numbers to be filled, at this point, any 4 can be chosen, to fill in four of these cells, each set of four numbers has 2 ways to fill,

so there are a total of $2 \times 2 \times C_{8}^{4} \times 2 \times 2=1120$ ways to fill.
Therefore, the answer is 1120.