  Recently, Z. W. Sun put forward a series of conjectures on monotonicity of
combinatorial sequences in the form of $\{z_n/z_{n-1}\}_{n=N}^\infty$ and
$\{\sqrt[n+1]{z_{n+1}}/\sqrt[n]{z_n}\}_{n=N}^\infty$ for some positive integer
$N$, where $\{z_n\}_{n=0}^\infty$ is a sequence of positive integers. Luca and
St\u{a}nic\u{a}, Hou et al., Chen et al., Sun and Yang proved some of them. In
this paper, we give an affirmative answer to monotonicity of another new kind
of number conjectured by Z. W. Sun via interlacing method for log-convexity and
log-concavity of a sequence, and we also use the criterion for log-concavity of
a sequence in the form of $\{\sqrt[n]{z_n}\}_{n=1}^\infty$ due to Xia.
