A024190 [ (2nd elementary symmetric function of 3,4,...,n+3)/(3+4+...+n+3) ].

1, 3, 6, 9, 13, 17, 22, 27, 33, 39, 46, 53, 60, 69, 77, 86, 96, 106, 117, 128, 140, 152, 165, 178, 191, 206, 220, 235, 251, 267, 284, 301, 319, 337, 356, 375, 394, 415, 435, 456, 478, 500, 523, 546