ABSTRACT We present the results of our ALMA observations of three active galactic nucleus (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 shows clear buried AGN signatures in the infrared. If the vibrational excitation is dominated by infrared radiative pumping, through the absorption of infrared 14 m 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.