Dedicated to my friend Tanishq Varshney

Calculus Level pending

\[\large{\left\lfloor \sum _{ n=1 }^{ 150 }{ \frac { { \left( -1 \right) }^{ n }\left( 2n+3 \right) ! }{ \left( \begin{matrix} { 4 }^{ n } \\ n+1 \end{matrix} \right) } } \right\rfloor =?}\]

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