A simple recursion equation

Question

Let $L_1=\lceil\log_2x\rceil$ where $x>0$, $L_i = \lceil \log_2L_{i-1} \rceil$ and let $T[1]=1$.

What is the solution for the recursion equation $$T[x]=\sum_{i=1}^{L_1}\frac{xT[L_1-i+1]}{2^i}?$$