Sum of Half Factorials!

Calculus Level 4

\[\large\frac{1}{\left(\frac{1}{2}\right)!}+\frac{1}{\left(\frac{3}{2}\right)!}+\frac{1}{\left(\frac{5}{2}\right)!}+\frac{1}{\left(\frac{7}{2}\right)!}+\cdots=\ ?\]

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