There are (n2 - n) / 2 moves required.

I am not aware that "stampled" is a word beyond a cross between stampede and trample, but I believe you wish to reverse the order of numbers from 1 to n where only two consecutive numbers can be swapped per step.

This process will show a pattern of triangular numbers. For example:

Let us suppose there are 3 numbers 1,2,3: To move the last (highest) number to the first place requires 2 steps. The second highest number is now in the last place. To move it to the second place requires 1 step. Finished. Total = 3 steps.

Or:

If there are 4 numbers, i.e. 1,2,3,4:

3 steps + 2 steps + 1 step = 6 steps total. We know it is only 3 steps more than the last example because once we have moved the 4 to the first place we then simply have to do the above again (rearrange the 1,2,3, to 3,2,1).

So you can see that the number of steps are all triangular numbers.

A triangular number is calculated by n(n+1) / 2. So we can use this formula, but we need to alter it because the number of steps are for the previous triangular number. E.g. Where there are 4 numbers we have to do 1+2+3 steps to reorder it (see above).

Therefore if we make our formula (n - 1) n / 2 = (n2 - n) / 2 then this will work.