A024180 [ (3rd elementary symmetric function of 2,3,...,n+3)/(2+3+...+n+3) ].

0, 2, 3, 5, 7, 10, 13, 16, 20, 24, 28, 32, 37, 42, 48, 54, 60, 67, 74, 81, 88, 96, 104, 113, 122, 131, 141, 151, 161, 171, 182, 193, 205, 217, 229, 242, 255, 268, 281, 295, 309, 324, 339