Table[(2^n)-2n+3,{n,0,10}]

{4,3,3,5,11,25,55,117,243,497,1007} // FindSequenceFunction

{1,0,0,0,0,0,0} // FindSequenceFunction

FindSequenceFunction[{4,3,3,5,11,25,55,117,243,497,1007}, n+1] // Simplify

Sum[((FindSequenceFunction[{4,3,3,5,11,25,55,117,243,497,1007}, n+1](t^n))/(n!)), {n,0,∞}]