A024402 [ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.

3, 20, 63, 150, 304, 552, 926, 1460, 2197, 3180, 4460, 6090, 8128, 10639, 13689, 17350, 21699, 26817, 32790, 39706, 47662, 56755, 67090, 78774, 91919, 106644, 123069, 141320, 161528, 183828, 208360, 235266, 264697, 296804, 331746, 369683, 410784