  We evaluate the symmetric functions $e_k$, $h_k$ and $p_k$ on the alphabet
$\{x_r/(1-tx_r)\}$ by elementary methods and give the related generating
functions. Our formulas lead to a new and short proof of an ex-conjecture of
Lassalle, which was proved by Lascoux and Lassalle in the framework of
$\lambda$-rings theory.
