2n factorial formula made accurate

You may be aware that I made 2n! formula of the type ((((n+1)(n+2))/2)^(n)). I have made it very approximate. 

The formula for (2n)! is

The Wolfram Alpha results to confirm that the formula is now very approximate. 

Have a nice weekend!!

(Today on September 8th, 2024)

If you are doing a programming in computer, then you may use the following.  The results will be more accurate.

I have been working on ((((n+1)(n+2))/2)^n) since April. 5 months. I derived the formula from Measuring Behavior expression or what I term it to be equivalent to Wallis pi. I was trying to get 0.5 factorial.  While doing that I discovered the above pattern for (2n)!. So a journey of 5 months of intense application ended yesterday night. 

Of course, James Stirling formula for n! is far more superior and has far more fidelity. 

But the expression (((n+1)(n+2))/2) is the sum of first (n+1) numbers. And that is the reason why I persisted with this formula.  Because sum of (n+1) numbers to the power n is related to 2n!. I found that interesting!!