2n factorial - Final submission

 The (2n)! formula with ((((n+1)(n+2))/2)^n) gave me many sleepless nights since April 2024. On April 2024, I discovered that ((((n+1)(n+2))/2)^n) is approximately connected to (2n)!. But how to give an expression? My education is limited. My mathematical prowess is hardly comparable to champions of IIT JEE.

But I felt it is my duty to complete the formula. Till calculator range. Till 170!. Or when n equals 85.

I carried on. I used the formula of Stirling formula and other expressions of (2n)! to get (2n)! through ((((n+1)(n+2))/2)^n). Well that was incorrect method. But I continued.

Now, I have finally made it. Without the use of any other approximate or accurate formula of (2n)!

Here is the formula

Here is an excel sheet that confirms 99 percent accuracy.

Have a great weekend folks!!