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A160739 16*P_6(n), 16 times the Legendre Polynomial of order 6 at n.

%I A160739 #26 Sep 08 2022 08:45:45
%S A160739 -5,16,10159,143824,867211,3415120,10373071,26425744,59271739,
%T A160739 120704656,227860495,404631376,683245579,1106013904,1727242351,
%U A160739 2615311120,3854919931,5549499664,7823790319,10826585296,14733641995,19750758736,26117017999
%N A160739 16*P_6(n), 16 times the Legendre Polynomial of order 6 at n.
%H A160739 G. C. Greubel, <a href="/A160739/b160739.txt">Table of n, a(n) for n = 0..1000</a>
%H A160739 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A160739 a(n) = 231*n^6 - 315*n^4 + 105*n^2 - 5. - _Vaclav Kotesovec_, Jul 31 2013
%F A160739 From _Colin Barker_, Jul 23 2019: (Start)
%F A160739 G.f.: -(5 - 51*x - 9942*x^2 - 73222*x^3 - 73047*x^4 - 10047*x^5 - 16*x^6) / (1 - x)^7.
%F A160739 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 A160739 (End)
%p A160739 A160739 := proc(n)
%p A160739         16*orthopoly[P](6,n) ;
%p A160739 end proc: # _R. J. Mathar_, Oct 24 2011
%t A160739 Table[16 LegendreP[6,n],{n,0,40}]
%o A160739 (PARI) a(n)=16*pollegendre(6,n) \\ _Charles R Greathouse IV_, Mar 18 2017
%o A160739 (PARI) Vec(-(5 - 51*x - 9942*x^2 - 73222*x^3 - 73047*x^4 - 10047*x^5 - 16*x^6) / (1 - x)^7 + O(x^30)) \\ _Colin Barker_, Jul 23 2019
%o A160739 (Magma) [231*n^6 -315*n^4 +105*n^2 -5: n in [0..30]]; // _G. C. Greubel_, May 02 2018
%Y A160739 Cf. A144126, A160741.
%K A160739 sign,easy
%O A160739 0,1
%A A160739 _N. J. A. Sloane_, Nov 17 2009