Just get start/end values from the form, and use them in a for() loop to create the query (or queries) needed to insert them into the database.
$start = (int) $_POST['start'];
$end = (int) $_POST['end'];
if($start <= $end)
{
for($sn = $start; $sn <= $end; $sn++)
{
$sql = "INSERT INTO table_name (serial_number) VALUES ($sn)";
$result = mysql_query($sql);
}
}
The above is, of course, minimal code that should be enhanced with more thorough validation and error-checking. It could also be enhanced to combine ranges of serial numbers in a set of insert values so as to reduce the number of queries required.