  We study coefficients $b_n$ that are expressible as sums over the Li/Keiper
constants $\lambda_j$. We present a number of relations for and representations
of $b_n$. These include the expression of $b_n$ as a sum over nontrivial zeros
of the Riemann zeta function, as well as integral representations. Conditional
on the Riemann hypothesis, we provide the asymptotic form of $b_n \sim
2^{-n-2}\ln n$.
