A024197 a(n) = 3rd elementary symmetric function of the first n+2 odd positive integers.

15, 176, 950, 3480, 10045, 24640, 53676, 106800, 197835, 345840, 576290, 922376, 1426425, 2141440, 3132760, 4479840, 6278151, 8641200, 11702670, 15618680, 20570165, 26765376, 34442500, 43872400, 55361475, 69254640, 85938426, 105844200, 129451505

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

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)^2*(n^2+3*n+1)/6.

G.f.: -x*(x^3+33*x^2+71*x+15) / (x-1)^7. - Colin Barker, Aug 15 2014

a(n) = A004320(n)*A028387(n). - R. J. Mathar, Oct 01 2016

a(n) = A028338(n+2, n-1), n >= 1, (fourth diagonal). See a crossref. below. - Wolfdieter Lang, Jul 21 2017

Prog

(PARI) Vec(-x*(x^3+33*x^2+71*x+15)/(x-1)^7 + O(x^100)) \\ Colin Barker, Aug 15 2014

Crossrefs

Contribution from Johannes W. Meijer, Jun 08 2009: (Start)

Equals fourth right hand column of A028338 triangle.

Equals fourth left hand column of A109692 triangle.

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

(End)

Sequence in context: A069379 A184285 A120995 * A210782 A071535 A081043

Adjacent sequences: A024194 A024195 A024196 * A024198 A024199 A024200

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved