Are you sure that is the correct sequence?
dy/dx=2,4,8,12,24
d2y/dx2=2,4,4,12
d3y/dx3=2,0,8
d4y/dx4=-2,8
So there is no constant rate of change so we cannot be certain what order of equation would continue the sequence accurately...
We COULD make d5y/dx5=10 so we COULD make a fifth order equation to create that sequence, however there is no way that we can prove that it is valid beyond the data points given...ie, there is no way to prove what the next term after 62 is.
If you wish to solve for that fifth order forced fit you can set up a system of equations of the form an^5+bn^4+cn^3+dn^2+en+f=a(n) using all of your points (n, a(n))