Did I find out something in my dreams? (I)

One day, I was asleep, and in my dream yesterday, I dreamt that I was playing with factorials. I then got this sudden revelation of a weird formula:

$\LARGE{\frac{1! × 2! × ... × n!}{1 × 2 × ... × 2n}}$

Simplifying this, we can get:

$\LARGE{\frac{G(n + 2)}{(2n)!}}$

Where $G(z)$ is the $\text{Barnes G-function}$ and $G(n + 2)$ is the superfactorial

When we substitute $n$ with different values, we gain these numbers:

$n = 3$	$0.01666…$
$n = 4$	$0.00714285…$
$n = 5$	$0.00952380…$
$n = 6$	$0.0519480…$
$n = 7$	$1.438561…$

I decided to plot this using WolframAlpha, but I do not have the Pro Version, so I plotted a smaller range of values instead (because I was bored a lot...)

Does this graph or number set have any special value to them? I was just bored, but maybe you can find a better explanation for these numbers. I would love to see what random facts you can gain about these weird numbers that came to me in a dream...

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Did I find out something in my dreams? (I)

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