Account numbers are not usually reallocated to anyone else. The cash should have been returned to the sender but it obviously hasn't been, the institution you sent it to probably has it held on a suspense account until they get round to trying to sort it out.
Don't worry, you haven't lost the cash. Three weeks seems a bit long though, get on to your bank and chase them up. Even if it has gone to someone else (which is highly unlikely), they are not allowed to keep money that isn't theirs!