#[05AB1E](http://github.com/Adriandmen/05AB1E), [4 bytes, Paul Picard](https://codegolf.stackexchange.com/a/77443/34388), [A001317](https://oeis.org/A001317)

Code:

 $Fx^

[Try it online!](http://05ab1e.tryitonline.net/#code=JEZ4Xg&input=OA)

Explanation:

 $ # Pushes 1 and input
 F # Pops x, creates a for-loop in range(0, x)
 x # Pops x, pushes x and 2x
 ^ # Bitwise XOR on the last two elements
 # Implicit, ends the for-loop
 # Implicit, nothing has printed so the last element is printed automatically

The sequence basically is a binary Sierpinski triangle:

 f(0)= 1 =1
 f(1)= 1 1 =3
 f(2)= 1 0 1 =5
 f(3)= 1 1 1 1 =15
 f(4)= 1 0 0 0 1 =17

And translates to the formula **a(n) = a(n - 1) XOR (2 × a(n - 1))**

Luckily, I remembered [this one](https://codegolf.stackexchange.com/a/67503/34388) :)