I learnt a lot of new words (Hall-Littlewood, Jack and Macdonald polynomials) but unfortunately everything I dug up is written without a single example and I still don't know the answer to a very obvious generalization: Let $P$ be a partition. Example: $31$. The symmetric polynomial corresponding to $P$ would be $f_{31}=a^3*b+a^3*c+...$ (with any number of variables: if we work in the ring of symmetric functions, it doesn't matter anyway). Now Newton's identities cover $f_{1...1}$ vs. $f_n$. I'd like to have an explicite formula or at least algorithm (at the moment I do it handish which is tedious and error-prone) to express any $f_P$ in the basis functions (actually I need the power sums $f_n$, but since the standard Newton identities cover the conversion, a formulation via the elementary symmetric polynomials is fine, either). Example with power sums: $f_{31}=f_3*f_1-f_4$.
P.S. The tag is probably not so brilliant, please amend it and then delete this PS.

I learnt a lot of new words (Hall-Littlewood, Jack and Macdonald polynomials) but unfortunately everything I dug up is written without a single example and I still don't know the answer to a very obvious generalization: Let $P$ be a partition. Example: $31$. The symmetric polynomial corresponding to $P$ would be $f_{31}=a^3*b+a^3*c+...$ (with any number of variables: if we work in the ring of symmetric functions, it doesn't matter anyway). Now Newton's identities cover $f_{1...1}$ vs. $f_n$. I'd like to have an explicit formula or at least algorithm (at the moment I do it by hand, which is tedious and error-prone) to express any $f_P$ in the basis functions (actually I need the power sums $f_n$, but since the standard Newton identities cover the conversion, a formulation via the elementary symmetric polynomials is fine, either). Example with power sums: $f_{31}=f_3*f_1-f_4$.