  Recently, Agievich proposed an interesting upper bound on binomial
coefficients in the de Moivre-Laplace form. In this article, we show that the
latter bound, in the specific case of a central binomial coefficient, is larger
than the one proposed by Sasvari and obtained using the Binet formula for the
Gamma function. In addition, we provide the expression of the next-order bound
and apply it to Catalan numbers $C_n$. The bounds are very close to the exact
value, the difference decreasing with $n$ and with the order of the upper
bound.
