SAT1000 - P924

Given that:

$\displaystyle \sum_{i=1}^{n} i^k = a_{k+1} n^{k+1} + a_k n^k + a_{k-1} n^{k-1} + a_{k-2} n^{k-2} + \cdots + a_1 n + a_0$

Then find the value of $\lfloor 10^7 (a_{k+1}+a_k+a_{k-1}+a_{k-2}) \rfloor$ at $k=2020$ .

Have a look at my problem set: SAT 1000 problems