You're going to need more specificity here. There are various "rights". An example:
A number of early Tarzan books by Edgar Rice Burroughs, including the original classic Tarzan of the Apes have long since lapsed into public domain, by U.S. copyright statutes, but the characters (notably the ApeMan his own self) are trademarked, and remain under that protection. You can, therefore, reprint freely Tarzan of the Apes and a number of other sequels, but you cannot legally write a new novel invoking the character of Tarzan, without obtaining permission of the trademark rights holders. I believe a similar situation exists with Sherlock Holmes, and Fu Manchu.
When you talk about a "series" in public domain, you need to be sure both the entire series of books AND the characters involved are really unprotected by copyrights and trademarks. E.R. Eddison's quirky classic fantasy series is another interesting example: the first novel, The Worm Ouroboros is in public domain in the U.S., but the subsequent volumes are not. AND, you need to be aware that copyright statutes vary between the U.S. and the E.U. (and Canada and Australia, as well). It's a complicated matter.
So, what work are you talking about?
caw