# Any idea for this

Algebra Level 5

$\large{\sum _{ k=0 }^{ \infty }{ { \left( -1 \right) }^{ k }\frac { \prod _{ r=0 }^{ k }{ { \left( 1+{ 4r }^{ 2 } \right) } } }{ { 9 }^{ k+1 }\left( 2k+2 \right) ! } } }$

If the above summation can be expressed as

${A \sin^{B} \bigg(\frac{\ln \big(\frac{C+\sqrt{D}}{E} \big)}{2}\bigg)}$

where $$A,B,C,D,E$$ are positive integers (need not be distinct) and $$D$$ being square free.

Find $$A+B+C+D+E$$

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