Electrical resistivity, magnetic susceptibility, and specific heat measurements on single crystals of La$Tr_2$Al$_{20}$ with $Tr$ = Mo and W revealed that these compounds exhibit superconductivity with transition temperatures $T_c$ = 3.22 and 1.81 K, respectively, achieving the highest values in the reported La$Tr_2$Al$_{20}$ compounds. There appears a positive correlation between $T_c$ and the electronic specific heat coefficient, which increases with increasing the number of $4d$- and $5d$-electrons. This finding indicates that filling of the upper $e_g$ orbitals in the $4d$ and $5d$ bands plays an essential role for the significant enhancement of the superconducting condensation energy. Possible roles played by the $d$ electrons in the strongly correlated electron phenomena appearing in $RTr_{2}$Al$_{20}$ are discussed.
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