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A024197 a(n) = 3rd elementary symmetric function of the first n+2 odd positive integers. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 8 15:21 EDT 2021. Contains 343666 sequences. (Running on oeis4.)