Try to find a copy of Bill Goforth's excellent book on H&R shotguns. He's the only one that has done the research that I know of.
Bill's book on H&R firearms has not been published as yet (Nov. 2010) - it should hit the shelves in early 2011. In the mean time - look up shotguns in the H&R Inc. section of the "Blue Book of Gun Values" by S. Fjestad for the current research on H&R firearms by Bill Goforth and Jim Hauff - you can use that to ID your shotgun. Serial Number alone is not enough info to ID the piece.