We report infrared spectra of protonated water clusters H
+(H
2O)
n (
n = 20-50) cooled by H
2 tagging. IR spectra show sharper features, validating the cooling effect of the H
2 attachment even for the large clusters. Furthermore, the H
2-mediated spectrum has indicated the origin of the first antimagic number (
n = 22), which is a dangling water molecule on the cluster surface [K. Mizuse, A. Fujii, J. Phys. Chem. Lett. 2 (2011) 2130]. On the other hand, for the second magic (
n = 28) and antimagic (
n = 29) number clusters, no apparent difference is observed by the H
2 tagging. IR spectra of Ar-tagged H
+(H
2O)
20-22 are also measured. These spectra also show sharper features, however, no signature for the dangling water molecule is seen in
n = 22. This result implies there are multiple isomer types in the
n = 22 cluster and the observable type might vary with the choice of the inert gas for tagging.