Hello, please consider the following.
The equation is
Assume that, on a given domain where the sum is defined,
is a solution of the equation and we will find a recursion formula for the , then
So the equation becomes
And this is equal to 0, so we can say that
It comes
So
We can go further to find a generic expression but only 3 non-zero terms were requested.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you