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

1,1

Links

Table of n, a(n) for n=1..23.

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.

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

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 *)

Prog

(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

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)

Sequence in context: A221449 A076377 A165374 * A027788 A112497 A220822

Adjacent sequences: A024195 A024196 A024197 * A024199 A024200 A024201

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved