How Can I Solve It!!

Determine all sequences (x1,....,x2011)(x_{1},....,x_{2011}) of positive integers such for every positive integer nn there is an integer a with

x1n+2x2n+....+2011x2011n=an+1+1x_{1}^{n}+2x_{2}^{n}+....+2011x_{2011}^{n}=a^{n+1}+1.

Find the sum of all of the entries of all of the sequences.

Note: Suppose the solutions are (1,2,3...,2011)(1,2,3...,2011) and(2,4,6,8,...,4022)(2,4,6,8,...,4022), then your answer will be 1+2+3+...+2011+2+4+6+....+4022=60691981+2+3+...+2011+2+4+6+....+4022=6069198

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