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
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).
Crossrefs
Cf. A160739.
Programs
-
Mathematica
Table[LegendreP[6,2n+1],{n,0,50}] (* N. J. A. Sloane, Nov 17 2009 *) -
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
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)
Extensions
Definition corrected by N. J. A. Sloane, Nov 17 2009