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

%I A144126 #17 Jul 23 2019 09:03:59
%S A144126 1,8989,213445,1651609,7544041,25289461,69125869,163456945,346843729,
%T A144126 676661581,1234422421,2131762249,3517093945,5582925349,8573842621,
%U A144126 12795158881,18622228129,26510424445,37005786469,50756327161
%N A144126 P_6(2n+1), the Legendre polynomial of order 6 at 2n+1.
%H A144126 Colin Barker, <a href="/A144126/b144126.txt">Table of n, a(n) for n = 0..1000</a>
%H A144126 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A144126 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
%F A144126 From _Colin Barker_, Jul 23 2019: (Start)
%F A144126 G.f.: (1 + 8982*x + 150543*x^2 + 346228*x^3 + 150543*x^4 + 8982*x^5 + x^6) / (1 - x)^7.
%F A144126 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.
%F A144126 (End)
%t A144126 Table[LegendreP[6,2n+1],{n,0,50}] (* _N. J. A. Sloane_, Nov 17 2009 *)
%o A144126 (PARI) a(n)=pollegendre(6,n+n+1) \\ _Charles R Greathouse IV_, Oct 25 2011
%o A144126 (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
%Y A144126 Cf. A160739.
%K A144126 nonn,easy
%O A144126 0,2
%A A144126 _Vladimir Joseph Stephan Orlovsky_, Sep 11 2008
%E A144126 Definition corrected by _N. J. A. Sloane_, Nov 17 2009