The fulvenallenyl cation (C7H5+) and its complex with an argon atom have been studied by explicitly correlated coupled cluster theory at the CCSD(T)-F12x (x = a, b) level and by the double-hybrid density functional B2PLYP-D. For the free cation, an accurate equilibrium structure has been established and ground-state rotational constants of A(0) = 8116.4 MHz, B-0 = 2004.3 MHz, and C-0 = 1606.9 MHz are predicted. The equilibrium dipole moment is calculated to be mu(e) = 1.305 D, with the positive end of the dipole at the acetylenic hydrogen site. Anharmonic wavenumbers of C7H5+ were obtained by combination of harmonic CCSD(T*)-F12a values and B2PLYP-D anharmonic contributions. The most intense vibration is the pseudoantisymmetric CC stretching vibration at 2083 cm(-1). The potential energy surface of the complex C7H5+center dot Ar is characterized by two energy minima of C-s symmetry which are separated by a very low energy barrier. The dissociation energy of the most stable structure is predicted to be D-0 = 530 +/- 30 cm(-1).