# 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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