A024387 [ (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 4}.

20, 319, 1850, 6962, 20344, 50198, 109666, 218483, 404885, 707740, 1178937, 1885998, 2914945, 4373393, 6393898, 9137529, 12797693, 17604194, 23827533, 31783445, 41837686, 54411045, 69984609, 89105263, 112391425, 140539035