  We explore the connection between the holographic Weyl anomaly and the
superconformal index in six-dimensional $(1,0)$ theories. Using earlier results
from holographic computations of the $\mathcal O(1)$ contributions $\delta a$
and $\delta(c-a)$ to the corresponding six-dimensional Weyl anomaly
coefficients, we derive a pair of differential operators that extracts these
values from the large-$N$ single-trace index. In doing so, we also highlight
the structure of these corrections in terms of group theory invariants of the
superconformal representations.
