A048034 Number of nonempty subsets of {1,2,...,n} in which exactly 3/5 of the elements are <= (n-3)/3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 45, 55, 220, 264, 312, 780, 910, 1050, 3465, 4220, 5100, 21420, 26775, 33117, 118104, 146300, 179340, 574644, 708477, 866019, 2899380, 3610540, 4463500, 15634300, 19623175, 24446565, 83635695