A024198 4th elementary symmetric function of the first n+3 odd positive integers.
105, 1689, 12139, 57379, 208054, 626934, 1646778, 3889578, 8439783, 17085783, 32645613, 59394517, 103613692, 174281212, 283927812, 449681892, 694529781, 1048818981, 1552033791, 2254874391, 3221672146, 4533175570, 6289743070
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
- Wolfdieter Lang, On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles, arXiv:1708.01421 [math.NT], August 2017.
Crossrefs
From Johannes W. Meijer, Jun 08 2009: (Start)
Equals fifth right hand column of A028338 triangle.
Equals fifth left hand column of A109692 triangle.
Equals fifth right hand column of A161198 triangle divided by 2^m.
(End)
Programs
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Mathematica
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{105,1689,12139,57379,208054,626934,1646778,3889578,8439783},30] (* Harvey P. Dale, May 28 2018 *) -
PARI
Vec(-x*(x^4+112*x^3+718*x^2+744*x+105)/(x-1)^9 + O(x^100)) \\ Colin Barker, Aug 15 2014
Formula
a(n) = n*(n+1)*(n+2)*(n+3)*(15*n^4+150*n^3+515*n^2+672*n+223)/360.
G.f.: -x*(x^4+112*x^3+718*x^2+744*x+105) / (x-1)^9. - Colin Barker, Aug 15 2014
a(n) = A000332(n+3) * (15*n^4+150*n^3+515*n^2+672*n+223)/15 . - R. J. Mathar, Oct 01 2016
a(n) = A(n+4, n-1), n >= 1 (fifth diagonal). See a crossref. below. - Wolfdieter Lang, Jul 21 2017
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9). - Wesley Ivan Hurt, Jul 09 2025