%I #37 Oct 16 2023 12:08:59

%S 4,39,159,445,1005,1974,3514,5814,9090,13585,19569,27339,37219,49560,

%T 64740,83164,105264,131499,162355,198345,240009,287914,342654,404850,

%U 475150,554229,642789,741559,851295,972780,1106824,1254264,1415964,1592815,1785735

%N 2nd elementary symmetric function of first n+1 positive integers congruent to 1 mod 3.

%H Vincenzo Librandi, <a href="/A024212/b024212.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_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = n*(n+1)*(9*n^2+9*n-2)/8.

%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - _Clark Kimberling_, Aug 18 2012

%F G.f.: (4 + 19*x + 4*x^2)/(1 - x)^5. - _Clark Kimberling_, Aug 18 2012

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

%F E.g.f.: exp(x)*x*(32+124*x+72*x^2+9*x^3)/8 = exp(x)*x*(2 + x)*(16 + 54*x + 9*x^2)/8.

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

%t Table[n(n+1)(9n^2+9n-2)/8,{n,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{4,39,159,445,1005},40] (* _Harvey P. Dale_, Oct 16 2023 *)

%o (Magma) [n*(n+1)*(9*n^2+9*n-2)/8: n in [1..40]]; // _Vincenzo Librandi_, Oct 10 2011

%Y Cf. A016777, A286718.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_