A048048 Number of nonempty subsets of {1,2,...,n} in which exactly 5/6 of the elements are <= (n+1)/3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 11, 66, 72, 78, 273, 294, 315, 840, 896, 952, 2142, 2268, 2394, 4959, 5230, 5502, 12012, 12705, 13409, 34914, 37224, 39600, 117975, 126412, 135135, 405405, 434434, 464464, 1309959, 1400455