I don't know about this seller, but I sometimes have difficulty seeing serial numbers well enough to write them down. Either I have to bend at an awkward angle or the light isn't good enough for my aging eyes. I am thinking there might be a legitimate reason why they are not sending you the serial # and they may not want to admit why.
Is there a specific reason why you need the serial #? I cannot imagine anyone stealing a longarm setup! I would perhaps call Nolting, explain the situation, and see if they can verify the information you have received so far.