A160743 - OEIS

%I #25 Jul 23 2019 10:48:55

%S 0,8,17593,389112,3169562,15694600,57385803,170880248,438565492,

%T 1005601032,2110507325,4124403448,7599974478,13331249672,22425272527,

%U 36386743800,57216718568,87526438408,130667379777,190878599672,273452459650,384919809288,533255710163

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

%H G. C. Greubel, <a href="/A160743/b160743.txt">Table of n, a(n) for n = 0..1000</a>

%H <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 a(n) = n*(429*n^6 - 693*n^4 + 315*n^2 - 35)/2. - _Vaclav Kotesovec_, Jul 31 2013

%F From _Colin Barker_, Jul 23 2019: (Start)

%F 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 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 (End)

%p A160743 := proc(n)

%p         8*orthopoly[P](7,n) ;

%p end proc: # _R. J. Mathar_, Oct 24 2011

%t Table[8 LegendreP[7,n],{n,0,50}]

%o (PARI) a(n)=pollegendre(7,n)<<3 \\ _Charles R Greathouse IV_, Oct 24 2011

%o (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 nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 17 2009