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A160743 8*P_7(n), 8 times the Legendre Polynomial of order 7 at n.

%I A160743 #25 Jul 23 2019 10:48:55
%S A160743 0,8,17593,389112,3169562,15694600,57385803,170880248,438565492,
%T A160743 1005601032,2110507325,4124403448,7599974478,13331249672,22425272527,
%U A160743 36386743800,57216718568,87526438408,130667379777,190878599672,273452459650,384919809288,533255710163
%N A160743 8*P_7(n), 8 times the Legendre Polynomial of order 7 at n.
%H A160743 G. C. Greubel, <a href="/A160743/b160743.txt">Table of n, a(n) for n = 0..1000</a>
%H A160743 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A160743 a(n) = n*(429*n^6 - 693*n^4 + 315*n^2 - 35)/2. - _Vaclav Kotesovec_, Jul 31 2013
%F A160743 From _Colin Barker_, Jul 23 2019: (Start)
%F A160743 G.f.: x*(8 + 17529*x + 248592*x^2 + 548822*x^3 + 248592*x^4 + 17529*x^5 + 8*x^6) / (1 - x)^8.
%F A160743 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.
%F A160743 (End)
%p A160743 A160743 := proc(n)
%p A160743         8*orthopoly[P](7,n) ;
%p A160743 end proc: # _R. J. Mathar_, Oct 24 2011
%t A160743 Table[8 LegendreP[7,n],{n,0,50}]
%o A160743 (PARI) a(n)=pollegendre(7,n)<<3 \\ _Charles R Greathouse IV_, Oct 24 2011
%o A160743 (PARI) concat(0, Vec(x*(8 + 17529*x + 248592*x^2 + 548822*x^3 + 248592*x^4 + 17529*x^5 + 8*x^6) / (1 - x)^8 + O(x^40))) \\ _Colin Barker_, Jul 23 2019
%K A160743 nonn,easy
%O A160743 0,2
%A A160743 _N. J. A. Sloane_, Nov 17 2009