Let dp[i] be "the maximum score to reach the end starting at index i". The answer for dp[i] is nums[i] + max{dp[i+j]} for 1 <= j <= k. That gives an O(n*k) solution.

Instead of checking every j for every i, keep track of the largest dp[i] values in a heap and calculate dp[i] from right to left. When the largest value in the heap is out of bounds of the current index, remove it and keep checking.