How can I recover a dropped table which is not in the recycle bin?
You can clone your production database to a point in time before the table was dropped, then export the table you need and import into your prod database. 
You can also try a table space point in time recovery. I tested it out a few years back, but I haven't needed to do it since.

Performing RMAN Tablespace Point-in-Time Recovery (TSPITR)