Thank you very much for such detailed explanation. Thank you again.

@Rivin: Thank you very much for the paper. In the paper author tried to estimate different $a_i$. From these estimates $\sum_{i=0}^n|a_i|$ is not easily followed for general $b$. Thank you again for your kind help.

@Stanley: Thank you very much. For $b\leq n/3$, I have tried similar approach but do not get anything better than $2^{n-b}$.

@Stanley: Thank you very much for your kind help. I have tried to understand main results from these papers. But there is no such closed form. I need closed form as a function of $b,n$ so that I can calculate upper bound on $\sum_{i=0}^n |a_i|$. Thank you again for your help.