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 ..

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