  The NA61/SHINE experiment at the CERN Super Proton Synchrotron (SPS) studies
the onset of deconfinement in hadron matter by a scan of particle production in
collisions of nuclei with various sizes at a set of energies covering the SPS
energy range. This paper presents results on inclusive double-differential
spectra, transverse momentum and rapidity distributions and mean multiplicities
of $\pi^\pm$, $K^\pm$, $p$ and $\bar{p}$ produced in the 20$\%$ most $central$
$^7$Be+$^9$Be collisions at beam momenta of 19$A$, 30$A$, 40$A$, 75$A$ and
150$A$ GeV/$c$. The energy dependence of the $K^\pm$/$\pi^\pm$ ratios as well
as of inverse slope parameters of the $K^\pm$ transverse mass distributions are
close to those found in inelastic $p$+$p$ reactions. The new results are
compared to the world data on $p$+$p$ and Pb+Pb collisions as well as to
predictions of the EPOS, UrQMD, AMPT, PHSD and SMASH models.
