A048001 Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= n/3.

0, 0, 0, 0, 0, 0, 2, 12, 18, 63, 168, 224, 504, 1014, 1270, 2420, 4620, 5742, 12012, 27027, 35035, 84119, 199304, 260064, 601664, 1339464, 1720944, 3755844, 8093214, 10329750, 22591800, 49876200, 64071194, 144780009