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

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• 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.

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)

Programs

PARI

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

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