We have synthesized 10 new iron oxyarsenides, K$Ln_2$Fe$_4$As$_4$O$_2$ ($Ln$ = Gd, Tb, Dy, and Ho) and Cs$Ln_2$Fe$_4$As$_4$O$_2$ ($Ln$ = Nd, Sm, Gd, Tb, Dy, and Ho), with the aid of lattice-match [between $A$Fe$_2$As$_2$ ($A$ = K and Cs) and $Ln$FeAsO] approach. The resultant compounds possess hole-doped conducting double FeAs layers, [$A$Fe$_4$As$_4$]$^{2-}$, that are separated by the insulating [$Ln_2$O$_2$]$^{2+}$ slabs. Measurements of electrical resistivity and dc magnetic susceptibility demonstrate bulk superconductivity at $T_mathrm{c}$ = 33 - 37 K. We find that $T_mathrm{c}$ correlates with the axis ratio $c/a$ for all 12442-type superconductors discovered. Also, $T_mathrm{c}$ tends to increase with the lattice mismatch, implying a role of lattice instability for the enhancement of superconductivity.
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