Hash Collision Probabilities
$n$ is the output size of the given hash function. To find a collision you try randomly generated $k$ different inputs. When we say the output size is $n$, it means that the output space has $2^n$ elements.

What you see on that website is the general case of the collision probability. We normally talk about the 50% probability (birthday attack) on the hash collisions as 

$$ k = \sqrt{2^n}$$
You can also see the general result from the birthday paradox.

To have birthday attack with 50% percentage you will need $k = 2^{128} \approx 4.0 × 10^{38}$ randomly generated differently input for a hash function with output size $n= 256$