A024221 [ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 3}.

12, 163, 891, 3256, 9340, 22757, 49254, 97430, 179537, 312394, 518402, 826655, 1274155, 1907129, 2782449, 3969144, 5550027, 7623415, 10304946, 13729509, 18053268, 23455784, 30142248, 38345805, 48329989, 60391250, 74861587, 92111285, 112551745