Polynomial Recursion

Algebra Level 5

A sequence of polynomials \(f_k(x)\) is defined as follows. \[f_0(x)=1;\ f_{k+1}(x)=f_k(x+1)+x^{k+1}, \ k=0,1,2,...\] Find the last 3 digits of the coefficient of \(x\) in \(f_{10}(x)\).