# [Jelly], <s>9</s> 8 bytes

    Œp§_2İ‘P

[Try it online!][TIO-k36qx0ep]

[Jelly]: https://github.com/DennisMitchell/jelly
[TIO-k36qx0ep]: https://tio.run/##y0rNyan8///opIJDy@ONjmx41DAj4P/h9kdNayL//4821AHCWB0wbQSmjXSMgTSQBIuDaBMgDSTB8sZAvmksAA "Jelly – Try It Online"

Uses the altered form of the closed form expression. Takes input as a list `[x,y,z]`.

```
Œp          Cartesian product of the list.
            (Each element, being an integer, is implicitly converted to a range.)
  §         Sum the items of each triplet,
   _2       subtract 2 from each sum,
     İ      take the reciprocal of each lowered sum,
      ‘     increment each reciprocal,
       P    and return the product of the increments reciprocals.
```