Hi y'all I need help on a question that CPhill had partially answered (but very well) I need help on the rest. Can anyone help? Thanks!

http://web2.0calc.com/questions/in-class-we-saw-that-the-sum-of-the-entries-of-row-n-of-pascal-s-triangle-is-2-n-in-this-problem-we-investigate-the-sums-of-the-squares