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A024392 a(n) = 3rd elementary symmetric function of the first n+2 positive integers congruent to 2 mod 3. 6

%I

%S 80,806,4040,14155,39655,95200,204036,400830,734910,1273910,2107820,

%T 3353441,5159245,7710640,11235640,16010940,22368396,30701910,41474720,

%U 55227095,72584435,94265776,121092700,153998650,194038650,242399430

%N a(n) = 3rd elementary symmetric function of the first n+2 positive integers congruent to 2 mod 3.

%H Vincenzo Librandi, <a href="/A024392/b024392.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F a(n) = n*(n+1)*(n+2)*(3*n+7)*(9*n^2+33*n+22)/48.

%F G.f.: -x*(80+246*x+78*x^2+x^3) / (x-1)^7 . - _R. J. Mathar_, Oct 08 2011

%t Table[n (n + 1) (n + 2) (3 n + 7) (9 n^2 + 33 n + 22) / 48, {n, 1, 50}] (* _Vincenzo Librandi_, Jul 07 2019 *)

%o (MAGMA) [n*(n+1)*(n+2)*(3*n+7)*(9*n^2+33*n+22)/48: n in [1..40]]; // _Vincenzo Librandi_, Jul 07 2019

%K nonn,easy

%O 1,1

%A _Clark Kimberling_

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Last modified August 12 00:34 EDT 2022. Contains 356067 sequences. (Running on oeis4.)