Trigger Series Emails (1 week, 2 week, etc) via Form

I want the ability to trigger a set of autoresponders after a user submits a form.

For instance:

1. Someone submits a form and then immediately receive a welcome email
2. A week later they receive a second email
3. 2 weeks after the initial signup they receive a third email

Any ideas on tools I could use to make this possible?