A144126 P_6(2n+1), the Legendre polynomial of order 6 at 2n+1.

1, 8989, 213445, 1651609, 7544041, 25289461, 69125869, 163456945, 346843729, 676661581, 1234422421, 2131762249, 3517093945, 5582925349, 8573842621, 12795158881, 18622228129, 26510424445, 37005786469, 50756327161

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 924*n^6 + 2772*n^5 + 3150*n^4 + 1680*n^3 + 420*n^2 + 42*n+1. - Vaclav Kotesovec, Jul 31 2013

From Colin Barker, Jul 23 2019: (Start)

G.f.: (1 + 8982*x + 150543*x^2 + 346228*x^3 + 150543*x^4 + 8982*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.

(End)

Mathematica

Table[LegendreP[6, 2n+1], {n, 0, 50}] (* N. J. A. Sloane, Nov 17 2009 *)

Prog

(PARI) a(n)=pollegendre(6, n+n+1) \\ Charles R Greathouse IV, Oct 25 2011
(PARI) Vec((1 + 8982*x + 150543*x^2 + 346228*x^3 + 150543*x^4 + 8982*x^5 + x^6) / (1 - x)^7 + O(x^30)) \\ Colin Barker, Jul 23 2019

Crossrefs

Cf. A160739.

Sequence in context: A230839 A339348 A251234 * A263062 A215198 A202531

Adjacent sequences: A144123 A144124 A144125 * A144127 A144128 A144129

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 11 2008

Extensions

Definition corrected by N. J. A. Sloane, Nov 17 2009

Status

approved