I purchased the software but never received a serial number in the email.

Hello,

Thank you for purchasing Bandicam.
My name is Zun, I'm a forum manager of Bandicam.

We had a problem between PayPal and Gmail server.
We sent your serial number about 8 hours ago.

We're really sorry for your inconvenience.
If you have any question about it, please contact bandicam@bandisoft.com

Best Regards,
Zun