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What you want is already built-in as SymmetricPolynomial[]: SymmetricPolynomial[3, Array[f, 4]] f[1] f[2] f[3] + f[1] f[2] f[4] + f[1] f[3] f[4] + f[2] f[3] f[4] SymmetricPolynomial[4, Array[f, 4]] f[1] f[2] f[3] f[4] but otherwise, Bill's suggestion can be vastly simplified using Sum[] and Product[]'s ability to take a list of indices: Sum[Product[...

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