  We present the results of our ALMA observations of three AGN-dominated nuclei
in optical Seyfert 1 galaxies (NGC 7469, I Zw 1, and IC 4329 A) and eleven
luminous infrared galaxies (LIRGs) with various levels of infrared estimated
energetic contributions by AGNs at the HCN and HCO+ J=3-2 emission lines. The
HCN and HCO+ J=3-2 emission lines are clearly detected at the main nuclei of
all sources, except for IC 4329 A. The vibrationally excited (v2=1f) HCN J=3-2
and HCO+ J=3-2 emission lines are simultaneously covered, and HCN v2=1f J=3-2
emission line signatures are seen in the main nuclei of two LIRGs, IRAS
12112+0305 and IRAS 22491-1808, neither of which show clear buried AGN
signatures in the infrared. If the vibrational excitation is dominated by
infrared radiative pumping, through the absorption of infrared 14 um photons,
primarily originating from AGN-heated hot dust emission, then these two LIRGs
may contain infrared-elusive, but (sub)millimeter-detectable, extremely deeply
buried AGNs. These vibrationally excited emission lines are not detected in the
three AGN-dominated optical Seyfert 1 nuclei. However, the observed HCN v2=1f
to v=0 flux ratios in these optical Seyferts are still consistent with the
intrinsic flux ratios in LIRGs with detectable HCN v2=1f emission lines. The
observed HCN-to-HCO+ J=3-2 flux ratios tend to be higher in galactic nuclei
with luminous AGN signatures compared with starburst-dominated regions, as
previously seen at J=1-0 and J=4-3.
