A048021 Number of nonempty subsets of {1,2,...,n} in which exactly 1/5 of the elements are <= (n-2)/3.

0, 0, 0, 0, 1, 5, 15, 30, 70, 141, 213, 405, 765, 1110, 2310, 4954, 7435, 16575, 35945, 52871, 113815, 240385, 346745, 744345, 1595433, 2299998, 5036862, 10959446, 15770601, 34636245, 75326163, 107787262, 236331302, 514828047