ASASSN-18am/SN 2018gk is a newly discovered member of the rare group of luminous, hydrogen-rich supernovae (SNe) with a peak absolute magnitude of M_V ≈ -20 mag that is in between normal core-collapse SNe and superluminous SNe. These SNe show no prominent spectroscopic signatures of ejecta interacting with circumstellar material (CSM), and their powering mechanism is debated. ASASSN-18am declines extremely rapidly for a Type II SN, with a photospheric-phase decline rate of ∼6.0 mag (100 d)^-1. Owing to the weakening of H I and the appearance of He I in its later phases, ASASSN-18am is spectroscopically a Type IIb SN with a partially stripped envelope. However, its photometric and spectroscopic evolution shows significant differences from typical SNe IIb. Using a radiative diffusion model, we find that the light curve requires a high synthesized ⁵⁶Ni mass M_Ni ∼0.4 M_⊙ and ejecta with high kinetic energy E_kin = (7-10) x 10⁵¹ erg. Introducing a magnetar central engine still requires M_Ni ∼0.3 M_⊙ and E-kin = 3 x 10⁵¹ erg. The high ⁵⁶Ni mass is consistent with strong iron-group nebular lines in its spectra, which are also similar to several SNe Ic-BL with high ⁵⁶Ni yields. The earliest spectrum shows 'flash ionization' features, from which we estimate a mass-loss rate of Ṁ ≈ 2 x 10^-4 M_⊙ yr^-1. This wind density is too low to power the luminous light curve by ejecta-CSM interaction. We measure expansion velocities as high as 17 000 km s^-1 for Hα, which is remarkably high compared to other SNe II. We estimate an oxygen core mass of 1.8-3.4 M_⊙ using the [O I] luminosity measured from a nebular-phase spectrum, implying a progenitor with a zero-age main-sequence mass of 19-26 M_⊙.