A generalized supercongruence of Kimoto and Wakayama

In 2006, Kimoto and Wakayama discussed one kind of Apéry-like numbers which occurs in a representation of the special value of the spectral zeta function, and proposed a supercongruence conjecture on the sum of these numbers. This supercongruence conjecture was first proved by Long, Osburn and Swisher. In this paper, we extend the result of Long, Osburn and Swisher to a supercongruence modulo p4, which was originally conjectured by Sun.