Summing up factorials (1)

Calculus Level 5

\[ \sum_{ r=0 }^{ \infty }{ \frac{ { (r!) }^{ 2 } }{ \left( 2r+1 \right)! } } = \frac{ a\pi }{ b\sqrt{ b } } \]

If the above equation is true for positive coprime square-free integers \( a\) and \( b \). Find the value of \( a+b \).

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