1.

What is the order of growth of the solution to the Quicksort-like recurrence F_N = N^2 + 1 + {1\over N} \sum_{1\le k \le N}(F_{k-1} + F_{N-k})F N ​ =N 2 +1+ N 1 ​ ∑ 1≤k≤N ​ (F k−1 ​ +F N−k ​ ) with F_0=0F 0 ​ =0?

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