  The 63Cu nuclear quadrupole resonance (NQR) frequency, nu_q, in the
multi-layered cuprates is calculated in the cluster model by the exact
diagonalization method. The charge imbalance between the outer CuO_2 plane (OP)
with apical oxygen (OA) and the inner plane (IP) without OA in three-layered
Tl2223 is estimated by comparing our results with the experimental nu_q. In
Tl-based cuprates with more than three layers, we predict a large enhancement
of the splitting of nu_q between OP and IP by taking into account the reduction
of bond length between Cu and OA and a resulting enhancement of the charge
transfer energy. Our results show that the NQR frequency is a useful quantity
to estimate the charge imbalance in the multi-layered cuprates.
