The number of edges in the $k$-dimensional cube $Q_k$ (which is an important structure in network design, but you don't need to know the structure to solve this) can be found by the recurrence relation: $e(Q_1) = 1$; $e(Q_n) = 2e(Q_{n-1}) + 2n-1$ for $n>2$. Use generating functions to solve this recurrence relation and determine the number of edges in the $k$-dimensional cube.
Any help would be great!