Easing function: Ease-out-in (opposite of Ease-In-Out) I'm seeking an easing function that is the twin of the popular Ease-In-Out easing function--

Desired Behaviour
Begins quickly, slows down in middle, ends quickly.
References
Keep your eye on the black portion of the screen in this Sonic Heroes Stage Intro animation. Notice how the black screen gives way quickly at first, slows down when the screen is half-revealed, then quickly disappears. https://youtu.be/pnLvwfvHCV4?t=71
Here's a quick reference of what the graph should look like 

My attempts at curve fitting and experimentation haven't given me the equation / function I need, unfortunately. Any help would be appreciated!

How about this:
$y(x) = (x^3-2x^2+x)m_0+(-2x^3+3x^2)+(x^3-x^2)m_1$
where $m_0$ and $m_1$ are two positive constants.
Bigger $m_0$ and $m_1$ will result in more wavy curve. Here are two examples:
Example 1: $m_0=m_1=3$ 

Example 2: $m_0=m_1=4$ 

