I have a summation from k = 1,..., n of (m-k+1)(n-k+1), and I would like to simplify this in terms of just m and n.. I know that I need to write out the sum first, so
sum = (mn) + (m-1)(n-1) + (m-2)(n-2) + ... + (m-n+1)(1),
(is this right?)
but I'm having trouble proceeding from this to the next step. Can anyone help?