This works, though it's a bit ugly:
dir >_ && type _ && type _ > a.txt
It's a little more flexible than some of the other solutions, in that it works statement-by-statement so you can use it to append as well. I use this quite a bit in batch files to log and display messages:
ECHO Print line to screen and log to file. >_ && type _ && type _ >> logfile.txt
Yes, you could just repeat the ECHO statement (once for the screen and the second time redirecting to the logfile), but that looks just as bad and is a bit of a maintenance issue. At least this way you don't have to make changes to messages in two places.
Note that _ is just a short filename, so you'll need to make sure to delete it at the end of your batch file (if you're using a batch file).