Question: [Gamma function](https://en.wikipedia.org/wiki/Gamma_function) is defined as

[![Gamma function definition](https://i.stack.imgur.com/ES8hs.png)](https://i.stack.imgur.com/ES8hs.png)

It is a well-known fact that for positive integers it coincides with a properly shifted factorial function: `Γ(n) = (n - 1)!`. However, a less famous fact is

> 
> Γ(1/2) = π1/2
> 
> 
> 

Actually, the Gamma function can be evaluated for all half-integer arguments, and the result is a rational number multiplied by π1/2. The formulas, as mentioned in Wikipedia, are:

[![Gamma function for half-integer arguments](https://i.stack.imgur.com/DrL55.png)](https://i.stack.imgur.com/DrL55.png) (for n > 0)

In this challenge, you should write code (program or function) that receives an integer `n` and returns the rational representation of **Γ(1/2 + n) / π1/2**, as a rational-number object, a pair of integers or a visual plain-text representation like `15/8`.

The numerator and denominator don't need to be relatively prime. The code should support values of `n` at least in the range -10 ... 10 (I chose 10 because 20! < 264 and 19!! < 232).

Test cases (taken from Wikipedia):

```
Input | Output (visual) | Output (pair of numbers)
0     | 1               | 1, 1
1     | 1/2             | 1, 2
-1    | -2              | -2, 1
-2    | 4/3             | 4, 3
-3    | -8/15           | -8, 15

```

Answer: 
Octave, 27 bytes
================

```
@(n)rats(gamma(n+.5)/pi^.5)

```

Built-ins all the way.

Test suite on [ideone](http://ideone.com/NkkEtR).
Mathematica, ~~17~~ 15 bytes
============================

```
(#-1/2)!/√π&

```

Uses factorial function since `gamma(n + 1/2) = (n - 1/2)!`.

There are only 12 characters now but it needs 15 bytes to be represented. The bytes are counted using UTF-8. `Sqrt = √` is 3 bytes from 5 bytes with `@` (2 bytes saved, thanks to @[CatsAreFluffy](https://codegolf.stackexchange.com/users/51443/catsarefluffy)) and `Pi = π` is 2 bytes (equal).

[![Example](https://i.imgur.com/RoGArxm.png)](https://i.imgur.com/RoGArxm.png)