Bill came along with the item.
TBH, its no big deal if the bill doesn't mention the serial no. for things like Portable HDD. Reason being, when you buy a Portable HDD, the drive itself will give you an option to check/activate the warranty the first time you use it. Once you do that, it registers your drive with WD/Seagates database and activates your warranty.
After that, if you ever need to RMA the drive, the warranty status is available with WD/Seagate so (IMO) they should not bother you with a bill at all, let alone one with the serial no. mentioned. I have never RMA'ed anything so not sure about this.
Having said that, if it would help you, I would be willing to PM you the invoice no. I recd. from Amazon for that order. If you buy the item and the Serial no. is not mentioned in the bill you receive, you can then give Amazon the invoice no. for my order and ask them to explain why my invoice clearly mentions the model, serial and part no. but yours doesn't...