Triple Summation?

Calculus Level 5

\(\displaystyle \LARGE \lim _{ h\rightarrow \infty }{ \left( \sum _{ i=1 }^{ i=h }{ \frac { \left( \left( \sum _{ j=1 }^{ j=i }{ \frac { \left( 2j+1 \right) ! }{ \prod _{ k=1 }^{ k=j }{ \left( 2k-1 \right) } } } \right) +2 \right) }{ { \left( (i+1)! \right)}^{ 2 } } } \right) } \)

If the answer can be expressed as \({e}^{a}-b\), select \(a+b\).

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