  We compute Gromov-Witten (GW) and Donaldson-Thomas (DT) invariants (and also
descendant invariants) for local CY 4-folds over Fano 3-folds, V_5 and V_22 up
to degree 3. We use torus localization for GW invariants computation, and use
classical results for Hilbert schemes on V_5 and V_22 for DT invariants
computation. From these computations, one can check correspondence between DT
and Gopakumar-Vafa (GV) invariants conjectured by Cao-Maulik-Toda in genus 0.
Also we can compute genus 1 GV invariants via the conjecture of Cao-Toda, which
turned out to be 0. These fit into the fact that there are no smooth elliptic
curves in V_5 and V_22 up to degree 3.
