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%I A024213 #23 Sep 08 2022 08:44:48
%S A024213 28,418,2485,9605,28700,72128,159978,322770,604560,1066450,1790503,
%T A024213 2884063,4484480,6764240,9936500,14261028,20050548,27677490,37581145,
%U A024213 50275225,66355828,86509808,111523550,142292150,179829000,225275778
%N A024213 a(n) = 3rd elementary symmetric function of first n+2 positive integers congruent to 1 mod 3.
%H A024213 Vincenzo Librandi, <a href="/A024213/b024213.txt">Table of n, a(n) for n = 1..10000</a>
%H A024213 Wolfdieter Lang, <a href="https://arxiv.org/abs/1708.01421">On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles</a>, arXiv:1708.01421 [math.NT], August 2017.
%H A024213 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A024213 a(n) = n*(n+1)*(n+2)*(3n+5)*(9n^2+21*n-2)/48.
%F A024213 G.f. -x*(28+222*x+147*x^2+8*x^3) / (x-1)^7 . - _R. J. Mathar_, Oct 08 2011
%F A024213 From _Wolfdieter Lang_, Jul 30 2017: (Start)
%F A024213 E.g.f.: x*exp(x)*(1344 + 8688*x + 10520*x^2 + 4122*x^3 + 594*x^4 + 27*x^5)/48.
%F A024213 a(n) = A286718(n+2, n-1), n >= 1. (End)
%o A024213 (Magma) [n*(n+1)*(n+2)*(3*n+5)*(9*n^2+21*n-2)/48: n in [1..30]]; // _Vincenzo Librandi_, Oct 10 2011
%Y A024213 Cf. A286718.
%K A024213 nonn,easy
%O A024213 1,1
%A A024213 _Clark Kimberling_

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