An INCREDIBLE Factorial-tastic Infinite Sum of n!²/2n! (Wolfram Alpha can't explain!)

An wonderful infinite sum with an equally spectacular solution, making use of various neat concepts such as Factorials, the Gamma Function, the Beta Function, Fubini's Theorem, a Geometric and Power Series, an interesting technique for Polynomial long division, Integration using Completing the Square, and Trig substitutions! If you are a fellow math enthusiast, you will be pleased :) Here's my previous video deriving the solution for the Sum(nxⁿ) mentioned in this tutorial: https://www.youtube.com/watch?v=m9ORChl2Q6I