Knowing that $A(x)=\sum_{i=0}^{\infty}a_ix^i, B(x)=\sum_{i=0}^{\infty}b_ix^i, C(x)=\sum_{i=0}^{\infty}c_ix^i$ express $$$$
a) $C$ as a function of $A$ and $B$ when $c_n=\sum_{j+2k\le n}a_jb_k $,
b) A as a function of $B$ when $nb_n=\sum_k^n2^k\frac{a_k}{(n-k)!}$
It is an exercise from the topic of generating functions, but is there a trivial connection between those 2?