Happy birthday George Boole

Compute upto 4 decimal places:-

$\large{\sum _{ n=2 }^{ \infty }{ \left( \frac { 1 }{ \left( \frac { { n }^{ 2 } }{ n-1 } \right) ! } \right) } }$

On 2nd November 2015 George Boole's 200th birthday was celebrated