A047173 Number of nonempty subsets of {1,2,...,n} in which exactly 2/3 of the elements are <= (n-1)/2.

0, 0, 0, 0, 3, 4, 12, 15, 40, 51, 135, 175, 455, 596, 1540, 2037, 5250, 7000, 18000, 24156, 62007, 83667, 214467, 290719, 744315, 1012935, 2590679, 3537703, 9039823, 12381252, 31612324, 43411489, 110761494, 152459010