I removed the inappropriate bracketing. Thank you for that point. 

However, it seems that at the 'ut(k,m)' line, Maple is hanging. It's been evaluating for about 5 minutes now on a relatively fast machine, and I really don't think the problem requires that much processing. When I insert that equation I am actually warned that there is an "ambiguity" and I am told to pick between the meaning of the expression being a "function definition" or "remember table assignment". If I pick the first, the equation doesn't use the sub-expressions that I defined. If I pick the second, the program executes "indefinitely". 

Any ideas on what may be the culprit?

This time I've attached my code: MapleMem4.mw