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%I #22 Oct 21 2022 21:10:25
%S 5,19,47,95,170,280,434,642,915,1265,1705,2249,2912,3710,4660,5780,
%T 7089,8607,10355,12355,14630,17204,20102,23350,26975,31005,35469,
%U 40397,45820,51770,58280,65384,73117,81515,90615,100455,111074,122512,134810,148010
%N [ (3rd elementary symmetric function of 3,4,...,n+4)/(3+4+...+n+4) ].
%H Vincenzo Librandi, <a href="/A024191/b024191.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F a(n) = n*(n+1)*(n^2+13n+46)/24 =a(n-1)+A005586(n). - _Henry Bottomley_, Oct 25 2001
%F G.f.: x*(5-6*x+2*x^2)/(1-x)^5.
%F a(n) = floor(A024184(n)/A055998(n+2)). - _R. J. Mathar_, Sep 15 2009
%F a(1)=5, a(2)=19, a(3)=47, a(4)=95, a(5)=170, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - _Harvey P. Dale_, Apr 28 2014
%t Table[n(n+1)(n^2+13n+46)/24,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{5,19,47,95,170},40] (* _Harvey P. Dale_, Apr 28 2014 *)
%t CoefficientList[Series[(5 - 6 x + 2 x^2)/(1 - x)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)
%o (PARI) a(n) = n*(n+1)*(n^2+13*n+46)/24 \\ _Charles R Greathouse IV_, Oct 21 2022
%Y a(n)=A115127(n+2, 3), n>=2.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_
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