What is the nth sequence?

Hi! We help with homework; we don't do it for you. With pi in your ID, I'm sure you can start. Let us know.

(PS- I spent about 3 minutes on it and didn't get it.)

Not a Fibonacci sequence. I tried a few other Nth sequences but no answer.

Could it be that the last number given should be 221 rather than 271? Just a guess...

There is a unique 4th degree polynomial P such that P(1) = 1, P(2) = 5, and P(n) would be the nth term of the sequence. Maybe that's it.