Expansion is tedious

Algebra Level 4

(1+x1!+x22!+x33!++xnn!)2\large \left( 1 + \dfrac{x}{1!} + \dfrac{x^2}{2!} + \dfrac{x^3}{3!} + \ldots + \dfrac{x^n}{n!} \right )^2

For n6n\geq 6, if the coefficient of x6x^6 in the expansion above can be expressed as ab\dfrac{a}{b} for coprime natural numbers a,ba,b, find a+b\sqrt{a+b} .


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