You can use something like this
for (( year = ${year_start}; year <=${year_end}; year++ ))
do
echo ${year}
done
seq
command is outdated and best avoided.
http://www.cyberciti.biz/faq/bash-for-loop/
And if you want real bad to use the following syntax,
for year in {${year_start}..${year_end}}
please modify it as follows:
for year in $(eval echo "{$year_start..$year_end}")
http://www.cyberciti.biz/faq/unix-linux-iterate-over-a-variable-range-of-numbers-in-bash/
Personally, I prefer using for (( year = ${year_start}; year <=${year_end}; year++ ))
.