Let f(x)=(1-x)^e (1+x)^{(n-e)}= \sum_{i=0}^n a_ix^i, where n is a positive integer and e is a non-negative integer less than n. I want to find an upper bound on \sum_{i=0}^n |a_i| other than the trivial upper bound 2^n. Also for e=0,1,\frac{n}{2}, it is easy. Is there any integration type of approach for this problem?