A160737 - OEIS

%I #19 Sep 08 2022 08:45:45

%S 0,4,743,6732,30046,94100,237429,517468,1014332,1834596,3115075,

%T 5026604,7777818,11618932,16845521,23802300,32886904,44553668,

%U 59317407,77757196,100520150,128325204,161966893,202319132,250338996,307070500,373648379

%N 4*P_5(n), 4 times the Legendre Polynomial of order 5 at n.

%H G. C. Greubel, <a href="/A160737/b160737.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = n*(63*n^4-70*n^2+15)/2. - _Vaclav Kotesovec_, Jul 31 2013

%F G.f.: x*(4+719*x+2334*x^2+719*x^3+4*x^4) / (x-1)^6 . - _R. J. Mathar_, May 06 2016

%p A160737 := proc(n)

%p         4*orthopoly[P](5,n) ;

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

%t Table[4 LegendreP[5,n],{n,0,50}]

%o (PARI) a(n)=4*pollegendre(5,n) \\ _Charles R Greathouse IV_, Mar 18 2017

%o (Magma) [n*(63*n^4-70*n^2+15)/2: n in [0..30]]; // _G. C. Greubel_, May 02 2018

%K nonn,easy

%O 0,2

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