A048069 Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= (n-4)/2.

0, 0, 0, 0, 0, 1, 6, 12, 42, 63, 168, 224, 504, 630, 1270, 1527, 2937, 3465, 6930, 8184, 18304, 21879, 54054, 65065, 165285, 198363, 491128, 584464, 1387744, 1636284, 3757884, 4398954, 9980054