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%I A024214 #18 Sep 08 2022 08:44:48
%S A024214 280,5714,45474,227969,859369,2662569,7141953,17147823,37702863,
%T A024214 77161513,148781633,272796342,479082422,810530182,1327228182,
%U A024214 2111584722,3274516506,4962843396,7368036676,10736476751,15381384711,21696600695
%N A024214 a(n) = 4th elementary symmetric function of first n+3 positive integers congruent to 1 mod 3.
%H A024214 Vincenzo Librandi, <a href="/A024214/b024214.txt">Table of n, a(n) for n = 1..10000</a>
%H A024214 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A024214 a(n) = n*(n+1)*(n+2)*(n+3)*(405*n^4+3510*n^3+9855*n^2+8814*n-184)/1920.
%F A024214 G.f. -x*(280+3194*x+4128*x^2+887*x^3+16*x^4) / (x-1)^9 . - _R. J. Mathar_, Oct 08 2011
%o A024214 (Magma) [n*(n+1)*(n+2)*(n+3)*(405*n^4+3510*n^3+9855*n^2+8814*n-184)/1920: n in [1..30]]; // _Vincenzo Librandi_, Oct 10 2011
%K A024214 nonn,easy
%O A024214 1,1
%A A024214 _Clark Kimberling_

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