How to exclude children categories of parent category

by 

$categories = get_categories( array(
    'exclude_tree' => array(40)
));

In both get_categories() and wp_list_categories() you can use the exclude_tree parameter instead of exclude.

  • exclude_tree
    (array|string) Array or comma/space-separated string of term ids to exclude along with all of their descendant terms. If $include is non-empty, $exclude_tree is ignored.
    Default empty array.