Help with infinite sequence. Need math whiz. Emergency?

Question

What is the general term (sigma notation: from 1 to infinity) for the sequence which begins 1; 2/(1*3); 4/(1*3*5); 8/(1*3*5*7)?

Very important and bugging the hell out of me

Answer 1

The n'th term here is
2^(n-1) / (2n-1)!!
where !! is the "double factorial" and is not the same as (n!)!.
For n even, n!! = n(n-2)(n-4)...6.4.2
For n odd, n!! = n(n-2)(n-4)...5.3.1

Answer 2

Try Un = 2^(2n-1) n! / (2n)! for integral n, n>=1

I don't think you can simplify any further - may others may have a better answer.