A048016 Number of nonempty subsets of {1,2,...,n} in which exactly 1/2 of the elements are <= (n-2)/3.

0, 0, 0, 0, 4, 5, 6, 27, 35, 44, 164, 219, 285, 1000, 1364, 1819, 6187, 8567, 11627, 38759, 54263, 74612, 245156, 346103, 480699, 1562274, 2220074, 3108104, 10015004, 14307149, 20160074, 64512239, 92561039, 131128139