On symmetric functions related to Witt vectors and the free Lie algebra (Q1842226)

Assume that \(h_n\) is the \(n\)-th complete symmetric function in infinitely many variables \(x_1, x_2,\ldots\), and define the symmetric functions \(q_n\) in the following way: \[ \prod_{n\ge 1} (1- q_n t)^{-1}= \sum_{n\ge 0} h_n t^n. \] The author shows that the functions \(- q_n\) are sums of Schur functions when \(n\) is a power of a prime number.