Solving second order difference equations with non-constant coefficients For the difference equation
  $$
2ny_{n+2}+(n^2+1)y_{n+1}-(n+1)^2y_n=0
$$
  find one particular solution by guesswork and use reduction of order to deduce the general solution.


So I'm happy with second order difference equations with constant coefficients, but I have no idea how to find a solution to an example such as this, and I couldn't find anything useful through Google or in my text book.

EDIT: I copied the question wrong, answers make more sense now I realise that ..
Let's look at the coefficients. We have $2n$, $n^2+1$, and $-(n+1)^2 = -n^2 - 2n - 1$. Do you notice anything particular about these three terms? Does that lead to the needed particular solution?
Hint: Write the equation as

$$2n(y_{n+2} - y_{n+1})= (n + 1)^2(y_{n} - y_{n+1})$$

or

$$2n A_{n+1} - (n+1)^2A_{n}$$

with solution

$$A_{n} = (n!)^2/ 2^{(n-1)}(n-1)!$$