How to define polynomials systematically?

[Diplo]

Dear all,
does someone know how to generate systematically (in n) the
polynomial x(1)+x(2)+...+x(n)?

Thanks.

[Aaron S. Meurer]

I am a little unclear on what you mean. Do you want something you can just plug the coefficients into, or is that supposed to represent evaluation? Could you give an example?

Aaron Meurer