A024400 [ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.
33, 304, 1418, 4726, 12760, 29771, 62375, 120293, 217192, 371635, 608125, 958252, 1461943, 2168809, 3139601, 4447759, 6181066, 8443406, 11356615, 15062445, 19724615, 25530979, 32695782, 41462024, 52103923, 64929482, 80283154, 98548608
Offset: 1