A047169 Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= n/2.

0, 0, 0, 0, 0, 0, 0, 0, 4, 5, 30, 36, 126, 147, 392, 448, 1008, 1134, 2304, 2565, 5115, 5687, 12342, 13860, 34320, 39039, 104104, 119119, 315679, 360815, 913640, 1039808, 2508928, 2842604