Polynomial Recursion

Algebra Level 5

A sequence of polynomials fk(x)f_k(x) is defined as follows. f0(x)=1; fk+1(x)=fk(x+1)+xk+1, k=0,1,2,...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 xx in f10(x)f_{10}(x).

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