Hi lpd,

On finding a recurrence relation, probably you want to start with

.

See what happens when you multiply everything out-- it should give you information about the coefficients of H(x).

A recurrence relation is not the same thing as finding an explicit expression for the coefficients. For example, if I write

then that's a recurrence relation. If I write

,

that's an explicit expression.

It's in finding an explicit expression for that you may find partial fractions useful.