Enumeration of permutations indexing local complete intersection Schubert varieties

We find the generating function for the permutation class ${\mathcal{A}}^{\mathrm{\prime }}=\text{Av}(52341,53241,52431,35142,42513,351624)$ whose permutations index local complete intersection Schubert varieties. The method we apply is the extension of how Albert and Brignall discover the generating function for $\mathcal{A}=\text{Av}(4231,35142,42513,351624)$ in their paper. This completes the enumerations of all classical permutation classes indexing certain types of Schubert varieties.