While messing around with zeta functions I encountered a strange sum:
$$
\sum\_{i=1}^{n} 11i^{10}-55i^9+165i^8-330i^7+462i^6 -462i^5+330i^4-165i^3+55i^2-11i+1 = n^{11}
$$

How should I approach proving that this equality is true for all $n,i \in \mathbb{N}$ ? I ran this for a few values on some engines and it does work for every number I tried.