Hello,

Let $B$ and $n$ be positive integers. Let $p_i \ge 0 $ be such that $\sum_{i=0}^{2B} p_i= 1$. I am interested in asymptotics (in terms of $B$, $n$, and $p_i$) for the coefficients of

$ (p_0 + p_1 x + p_2 x^2 + \dots + p_{2B}x^{2B})^n. $

Of particular interest to me is the central coefficient, i.e., that of $x^{Bn}$. Do you know of any references on this?

Thanks,

Pooya