  In this paper we present an effective method for computing certain real
coefficients $\lambda_{n}$ which appear in a criterion for the Riemann
hypothesis proved by Xian-Jin Li. With the use of this method a sequence of
over three-thousand $\lambda_{n}$'s has been calculated. This sequence reveals
a peculiar and unexpected behavior: it can be split into a strictly growing
\textit{trend} and some tiny \textit{oscillations} superimposed on this trend.
