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%I #25 Jan 09 2024 16:04:25
%S 2,11,29,61,115,196,312,474,690,971,1331,1781,2335,3010,3820,4782,
%T 5916,7239,8771,10535,12551,14842,17434,20350,23616,27261,31311,35795,
%U 40745,46190,52162,58696,65824,73581,82005,91131,100997,111644,123110,135436
%N a(n) = floor((3rd elementary symmetric function of 2,3,...,n+3)/(2+3+...+n+3)).
%H Ivan Neretin, <a href="/A024178/b024178.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-5,6,-4,1).
%F G.f.: x*(x^3 - 3x^2 + 3x + 2)/((1-x^3)*(1-x)^4).
%F a(n) = floor((1/24)*n*(n+1)*(n^2 + 9*n + 22)). - _Ivan Neretin_, May 21 2018
%t s[n_] := 1 + Range[n + 2]
%t Table[Floor[SymmetricPolynomial[3, s[n]]/SymmetricPolynomial[1, s[n]]], {n, 1,
%t 46}] (* _Clark Kimberling_, Sep 23 2016 *)
%t LinearRecurrence[{4,-6,5,-5,6,-4,1},{2,11,29,61,115,196,312},40] (* _Harvey P. Dale_, Dec 05 2018 *)
%K nonn
%O 1,1
%A _Clark Kimberling_
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