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tokens: signatures, it will also be important to better explore problems such as disk formation, the formation of disk outflows, and the termination of accretion by means of multidimensional simulations in the future. We note that the fallback accretion energy is more likely to be activated in hydrogen-rich progenitors from the perspective of stellar evolution. It is hard to achieve the conditions required to form magnetars in hydrogen-rich progenitors (e.g., Heger et al. 2005 ) because of efficient angular momentum transport from the core to the hydrogen-rich envelope, in particular if dynamo action is considered. For fallback-powered SNe, one needs to form an accretion disk near the compact remnant to have the accretion disk wind powering the SNe. Such an accretion disk can be formed even if the initial rotational period of the core is small because shells farther out in the envelope have higher specific angular momentum and can easily reach Keplerian velocities before being accreted onto the central compact object. Even if the angular momentum in the envelope is not sufficiently large, asymmetric explosions may impart sufficient angular momentum to the outer envelope by imparting some tangential velocity onto the fallback material, as found in a more energetic fallback supernova model (C. Chan et al. 2019, in preparation), which is enough to make an accretion disk as it falls back. Fallback-powered SNe may also be affected by the interaction between SN ejecta and a dense circumstellar medium (CSM) surrounding them. Although the 40 progenitor we studied does not experience much mass loss during its evolution, more massive progenitors are expected to undergo significant mass loss before the explosions due to the pulsational pair instability (Woosley 2017 ). After forming a dense CSM due to the pulsational pair instability, the progenitors are expected to collapse by forming BHs and may result in the fallback-powered SNe. Therefore, the existence of a dense CSM could be common in the fallback-powered SNe. The possibility of CSM interaction in fallback SNe needs to be studied further in the future. Difference in CSM configurations with the same central engine can result in a variety of LCs (e.g., Fischer et al. 2018 ). Finally, fallback-powered SNe may be common among the explosions of the first stars. It has been predicted that the first stars have a top-heavy initial mass function (e.g., Hirano et al. 2015 ), and many of them are likely to be massive enough to form a BH during their explosions. Pair-instability SNe from the first stars (Heger Woosley 2002 ) are generally considered as potential SNe that could become bright enough to be observed even from this early epoch of cosmic evolution in the future transient surveys, especially in near-infrared (e.g., Scannapieco et al. 2005 ). We have shown that the fallback-powered SN from the 40 first star can be as luminous as pair-instability SNe. The mass range of pair-instability SNe that can be as