The quotes around the table name and column name should be backquotes and not apostrophes (single quotes). Also, you should use the escape_string() function on the username before including it, or else if a username has a special character it will cause an error. So maybe this:
PHP Code:
$vbulletin->db->query_write("INSERT INTO `table` (`column`) VALUES ('".$vbulletin->db->escape_string($vbulletin->userinfo['username'])."')");