A024389 [ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 4}.

2, 19, 72, 190, 409, 773, 1336, 2159, 3309, 4863, 6907, 9532, 12840, 16939, 21945, 27985, 35189, 43699, 53664, 65239, 78591, 93891, 111320, 131067, 153328, 178309, 206221, 237286, 271732, 309795, 351722, 397763, 448180, 503242, 563224, 628413