someone please help me with this infinite sequence

[pakmingki]

1. The problem statement, all variables and given/known data
1,1,-1,3,-15,105,-945 ...

find an expression for the nth term


3. The attempt at a solution

I HAVE TO FIND THE PATTERN
Now, i know for a fact that there has to be a factorial in there somewhere, because n starts at 0, and as you can see every term is alternating except for the first 2, which means there has to be some kind of factorial in the formula.

This is in fact a secondary question. I am trying to find a formula for the nth derivative of sqrt(x+1) and knowing the formula for this sequence is crucial to finding the formula for the nth derivative.

So far i have:
there must be some factorial in there
its not an arithmetic sequence
its not a geometric sequence.

PLEASE HELP ME!!!

[Dick]

The symbol you are looking for is n!!. It's called a double factorial. It's defined recursively by n!!=(n)*(n-2)!!. So e.g. 7!!=1*3*5*7. Wikipedia actually has a lucid entry on it under Factorial.

[pakmingki]

hmm, trhat was a good idea, but how do i make it work to fit the sequenece?
ive been trying and i CANNOT get the numbers to fit into the double factorial.

[Dick]

1=1!!
3=3!!
15=5!!
105=7!!
945=9!!

I'm not quite seeing the problem here.

[Dick]

Maybe you want to write something like (2n-1)!!?

[pakmingki]

hmmmm
but look at the sequence.

When n = 7, the value is 9!!
when n = 6, the value is 7!!
when n = 5, the value is 5!!

[Dick]

Ok, so I would call that (2n-5)!!. The sequence is clear. You just have to fit the formula to it.

[pakmingki]

thanks for your help
but i got it

it's (-1)^(n+1) * (2n-3)!!

it doesnt work for 0, but for my purposes, that does not matter to me.

BUt the idea for the double factorial saved my life.

Thanks
i love you