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[ (2nd elementary symmetric function of 3,4,...,n+3)/(3+4+...+n+3) ].
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%I #11 May 02 2018 09:39:09

%S 1,3,6,9,13,17,22,27,33,39,46,53,60,69,77,86,96,106,117,128,140,152,

%T 165,178,191,206,220,235,251,267,284,301,319,337,356,375,394,415,435,

%U 456,478,500,523,546

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

%H Ivan Neretin, <a href="/A024190/b024190.txt">Table of n, a(n) for n = 1..10000</a>

%F Empirical g.f.: -x*(x^12 -2*x^11 +x^10 -2*x^9 +2*x^8 +2*x^6 -x^5 -x^3 +x^2 +x +1) / ((x -1)^3*(x^2 +1)*(x^2 +x +1)*(x^4 -x^2 +1)). - _Colin Barker_, Aug 16 2014

%t Table[Floor[1/12 x (106 + 35 x + 3 x^2)/(6 + x)], {x, 44}] (* _Ivan Neretin_, May 02 2018 *)

%K nonn

%O 1,2

%A _Clark Kimberling_