I am unable to find the formula for this given sequence:

Question

{2, -6/4, 24/16, -120/64, 720/256,...}

So far, I know it's at least this:

a(sub(n)) = ((-1)^(n+1))/(4^(n-1))

Basically, all I'm having trouble with is finding the pattern between the numerators. If anybody can help me with this, I would be grateful. Thanks!

Answer 1

Looks to me like

a_n = (-1)^(n-1) (n+1)!/4^(n-1)