How to run nohup and write its pid file in a single bash statement

This should work:

nohup ./myprogram.sh > /dev/null 2>&1 &
echo $! > run.pid

You already have one ampersand after the redirect which puts your script in background. Therefore you only need to type the desired command after that ampersand, not prefixed by anything else:

nohup ./myprogram.sh > /dev/null 2>&1 & echo $! > run.pid