[function.unserialize]: Error at offset
It looks as though you have invalid serialized data for that authorize_filetransfer_connection_settings_ftp variable.

If saving to the db manually, make sure you have serialized the data prior to db storage.

Some ways to set the variable include

variable_set('authorize_filetransfer_connection_settings_ftp', $value);

and

drush vset authorize_filetransfer_connection_settings_ftp 'value'

The former is a bit easier if setting an array value, otherwise you can do something like this with Drush:

drush php-eval 'variable_set("authorize_filetransfer_connection_settings_ftp",array("key1" =&gt; "value1", "key2" =&gt; "value2"));'