How can we have a call automatically transfer to a number after the call is ended?

I am not sure if we support this workflow (as far as redirecting a call after a call has been terminated, since it would be considered "Call Ended" in our system).

Using our touch tone commands, you can forward a call to another number (such as an IVR), but I an unaware of a programmatic way to do this using our API: http://success.ringcentral.com/articles/RC_Knowledge_Article/1169

You can do this with RingCentral's Contact Center (http://www.ringcentral.com/contact-center/overview.html) but you would need to contact your account executive to help you with this (also, this is not supported via our API currently).