The nonadiabatic excited-state molecular dynamics (NA-ESMD) method and excited-state instantaneous normal modes (ES-INMs) analyses have been applied to describe the state-specific vibrations that participate in the unidirectional energy transfer between the coupled chromophores in a branched dendrimeric molecule. Our molecule is composed of two-, three-, and four-ring linear poly(phenyleneethynylene) (PPE) units linked through meta-substitutions. After an initial laser excitation, an ultrafast sequential S-3 -> S-2 -> S-1 electronic energy transfer from the shortest to longest segment takes place. During each S-n -> Sn-1 (n = 3, 2) transition, ES-INM(S-n) and ES-INM(Sn-1) analyses have been performed on S-n and Sn-1 states, respectively. Our results reveal a unique vibrational mode localized on the S-n state that significantly matches with the corresponding nonadiabatic coupling vector d(n,(n-1)). This mode also corresponds to the highest frequency ES-INM(S-n) and it is seen mainly during the electronic transitions. Furthermore, its absence as a unique ES-INM(Sn-1) reveals that state-specific vibrations play the main role in the efficiency of the unidirectional S-n -> Sn-1 electronic and vibrational energy funneling in light-harvesting dendrimers.