A048014 Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= (n-1)/3.

0, 0, 0, 0, 0, 1, 2, 12, 42, 63, 168, 378, 504, 1014, 1914, 2420, 4620, 9295, 12012, 27027, 63083, 84119, 199304, 456484, 601664, 1339464, 2896664, 3755844, 8093214, 17441739, 22591800, 49876200, 111029050, 144780009