[sally-cj]

[EDIT] Here it is, fully tested and working:

$current_page = get_query_var('paged');
$current_page = max( 1, $current_page );

$per_page = 12;
$offset_start = 1;
$offset = ( $current_page - 1 ) * $per_page + $offset_start;

$post_list = new WP_Query(array(
    'cat'            => -15,
    'posts_per_page' => $per_page,
    'paged'          => $current_page,
    'offset'         => $offset, // Starts with the second most recent post.
    'orderby'        => 'date',  // Makes sure the posts are sorted by date.
    'order'          => 'DESC',  // And that the most recent ones come first.
));

// Manually count the number of pages, because we used a custom OFFSET (i.e.
// other than 0), so we can't simply use $post_list->max_num_pages or even
// $post_list->found_posts without extra work/calculation.
$total_rows = max( 0, $post_list->found_posts - $offset_start );
$total_pages = ceil( $total_rows / $per_page );

if ( $post_list->have_posts() ):
    while ( $post_list->have_posts() ):
        $post_list->the_post();


        // loop output here
    endwhile;

    echo paginate_links( array(
        'total'   => $total_pages,
        'current' => $current_page,
    ) );
endif;
wp_reset_postdata();

PS: The code was re-indented using tabs.

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