Tracy and Charlie

Tracy is teaching Charlie maths via a game called $N$-Cube, which involves three sections involving $N$. Tracy gives Charlie a number $N$, and Charlie makes a list of $N$-th powers of integers in increasing order $1^N, 2^N, 3^N, \dot, \text{so on}$. This teaches him exponentiation. Then Charlie performs the following subtraction game $N$ times: Take all pairs of consecutive numbers in the list a