Interesting, I had not seen that kind of generating function discussed before, so quite likely nobody ever invented a terminology for it. "Lacunary series" is a term for "sparse power series" of that general ilk, though. I doubt this kind of series is very useful for the sort of combinatorial purposes GFs usually are used for. You mentioned a few cute examples, sure, but they seem likely to me to be about the best you'll ever get, in which case, combinatoricists should not be very interested. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)