Understanding Battery rating
That "3400-A/s" may be the model number or serial number of a particular research cell which is being described.  I looked through that section of the Linden book and 3400-A/s isn't mentioned again in the text.  The author borrowed a table from a research paper to use as a "representative example" of an Li(Si)/FeS2 cell.

The way the caption is worded doesn't seem to mean they are giving a technical spec in amps per second.  If they were, there wouldn't be a dash between 3400 and A/s.  Amps per second wouldn't make sense to talk about in most cases, as it represents coulombs per second squared, the "acceleration" of charge rather than "velocity."  Like slew rate for current.