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According to many commenters at Ask SQL Server Central, if you don't have a back-up, you're going to be out of luck.
However, one person writes, "There is an outside chance of getting the data if your O/S backup had an open file agent. Ask your backup team if they can restore from prior to the issue to a test environment and you may be able to get the data."
It's pretty much the same conclusion here: Forget about it, unless..."If the DROP TABLE was executed from within a transaction and that transaction has not yet been committed, you can roll it back."
Beyond that, some people suggest purchase or downloading a free trial version of a third-party product that is able to read the log file and reconstuct the table from that information.