Finding recurrence relations for dynamic programming algorithms
If all of your values start out unstored, then $T(n) = n + T(1) + T(2) + \cdots + T(n - 1)$ still, however, when computing $T(n - 1)$, $T(1)$ through $T(n - 2)$ have already been found, so $T(n - 1) = n - 1 + O(1)$. Same for $T(1)$ through $T(n - 2)$ ($T(1)$ is just $O(1)$). This gives an overall runtime of
$$T(n) = n + O(1) + (1 + O(1)) + \cdots + (n - 1 + O(1)) = \frac{n(n-1)}{2}+n(1+O(1))=O(n^2)$$