Counting Constrained 3D Lattice Paths

Kelvin the frog is at the point $(0,0,0)$ and wishes to reach the point $(3,3,3)$. In a single move, he can either increase any single coordinate by $1$, or he can decrease his $z$-coordinate by $1$. Given that he cannot visit any point twice, and that at all times his coordinates must all stay between $0$ and $3$ (inclusive), compute the number of distinct paths Kelvin can take to reach $(3,3,3)$.