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.
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