Taxi route counts #5

$d=3$ and $\vec{V}=(1,1,1)$ , where $n$ is a positive integer.

There are a positive integer number, $d$ , of independent vectors, $\vec{V}_i$ , where $i$ runs from 1 to $d$ . A trip starts from the appropriate $\vec{0}$ of $d$ components and goes to a destination vector of $d$ positive integer components. A step of a trip consists of adding $1$ to a single component of the taxi's current position vector which was initially $\vec{0}$ of $d$ components. How many distinct routes would accomplish this trip?