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a(n) = 3rd elementary symmetric function of the first n+2 odd positive integers.
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%I #21 Dec 16 2017 15:29:42

%S 15,176,950,3480,10045,24640,53676,106800,197835,345840,576290,922376,

%T 1426425,2141440,3132760,4479840,6278151,8641200,11702670,15618680,

%U 20570165,26765376,34442500,43872400,55361475,69254640,85938426,105844200,129451505

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

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

%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.

%F a(n) = n*(n+1)*(n+2)^2*(n^2+3*n+1)/6.

%F G.f.: -x*(x^3+33*x^2+71*x+15) / (x-1)^7. - _Colin Barker_, Aug 15 2014

%F a(n) = A004320(n)*A028387(n). - _R. J. Mathar_, Oct 01 2016

%F a(n) = A028338(n+2, n-1), n >= 1, (fourth diagonal). See a crossref. below. - _Wolfdieter Lang_, Jul 21 2017

%o (PARI) Vec(-x*(x^3+33*x^2+71*x+15)/(x-1)^7 + O(x^100)) \\ _Colin Barker_, Aug 15 2014

%Y Contribution from _Johannes W. Meijer_, Jun 08 2009: (Start)

%Y Equals fourth right hand column of A028338 triangle.

%Y Equals fourth left hand column of A109692 triangle.

%Y Equals fourth right hand column of A161198 triangle divided by 2^m.

%Y (End)

%K nonn,easy

%O 1,1

%A _Clark Kimberling_