What is the value of

1*2 / 3! + (2*2^2)/4! + (3*2^3)/5! ............... (15*2^15)/17!

I tried making a general term for this but was unable to proceed further with that method. Secondly I multiplied the sum by 2 and tried to subtract it from the original (AP-GP sort of a method) but that is also not taking me any further.

Please guide me on this.

Thanks