A048036 Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= (n-3)/3.

0, 0, 0, 0, 0, 1, 6, 21, 42, 112, 252, 378, 759, 1419, 1914, 3564, 6864, 9295, 20020, 45055, 63083, 146648, 331568, 456484, 1007454, 2156994, 2896664, 6165494, 13079094, 17441739, 37871064, 82898739, 111029050, 247813500