  In this article we study large central charge partition function and
entanglement entropy of $T\bar{T}$ deformed two dimensional conformal field
theory, following the approach to $T\bar{T}$ deformation as integrated
infinitesimal double trace deformation used by Guica et al.. For sphere
partition function and entanglement entropy of half great circle with antipodal
points being the entangling surface, we obtain different results compared to
previous works, with more reasonable CFT limits and qualitatively different
behaviour as the deformation parameter $\mu$ goes to infinity, which
contradicts the simple version of the cutoff AdS holography proposal. For a
modified version of cutoff AdS holography which is supposed to work only in the
sector of classical pure gravity, we show that the flow equation of the metric
and one point function of energy-momentum tensor in $T\bar{T}$ deformation
corresponds to the flow equation of the boundary metric and Brown-York tensor
on a cutoff surface in AdS space as the cutoff surface moves in the direction
of normal geodesics. In addition the flow equation of gravity on-shell action
takes the form of $T\bar{T}$ deformation, with straightforward generalization
to higher dimensions. As an example we give a holographic computation of the
sphere partition function of $T\bar{T}$ CFT.
