A024213 - OEIS

%I #27 May 18 2026 16:58:21

%S 28,418,2485,9605,28700,72128,159978,322770,604560,1066450,1790503,

%T 2884063,4484480,6764240,9936500,14261028,20050548,27677490,37581145,

%U 50275225,66355828,86509808,111523550,142292150,179829000,225275778,279912843,345170035,422637880,514079200

%N a(n) = 3rd elementary symmetric function of first n+2 positive integers congruent to 1 mod 3.

%H Vincenzo Librandi, <a href="/A024213/b024213.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 <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+5)*(9*n^2+21*n-2)/48.

%F G.f. -x*(28+222*x+147*x^2+8*x^3) / (x-1)^7 . - _R. J. Mathar_, Oct 08 2011

%F From _Wolfdieter Lang_, Jul 30 2017: (Start)

%F E.g.f.: x*exp(x)*(1344 + 8688*x + 10520*x^2 + 4122*x^3 + 594*x^4 + 27*x^5)/48.

%F a(n) = A286718(n+2, n-1), n >= 1. (End)

%t A024213[n_] := n*(n + 1)*(n + 2)*(3*n + 5)*(9*n^2 + 21*n - 2)/48;

%t Array[A024213, 30] (* _Paolo Xausa_, May 18 2026 *)

%o (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 Cf. A286718.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_