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 approximate to -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 similar to 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 Ni-56 mass M-Ni similar to 0.4 M-circle dot and ejecta with high kinetic energy E-kin = (7-10) x 10(51) erg. Introducing a magnetar central engine still requires M-Ni similar to 0.3 M-circle dot and E-kin = 3 x 10(51) erg. The high Ni-56 mass is consistent with strong iron-group nebular lines in its spectra, which are also similar to several SNe Ic-BL with high Ni-56 yields. The earliest spectrum shows 'flash ionization' features, from which we estimate a mass-loss rate of (M) over dot approximate to 2 x 10(-4 )M(circle dot) 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 H alpha, which is remarkably high compared to other SNe II. We estimate an oxygen core mass of 1.8-3.4 M-circle dot 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-circle dot.