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A160741 Numerator of P_6(2n), the Legendre polynomial of order 6 at 2n.

%I A160741 #20 Jul 23 2019 08:28:55
%S A160741 -5,10159,867211,10373071,59271739,227860495,683245579,1727242351,
%T A160741 3854919931,7823790319,14733641995,26117017999,44040338491,
%U A160741 71215667791,111123125899,168143944495,247704167419,356428995631,502307776651,694869638479,945369767995
%N A160741 Numerator of P_6(2n), the Legendre polynomial of order 6 at 2n.
%H A160741 G. C. Greubel, <a href="/A160741/b160741.txt">Table of n, a(n) for n = 0..1000</a>
%H A160741 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A160741 From _Colin Barker_, Jul 23 2019: (Start)
%F A160741 G.f.: -(5 - 10194*x - 795993*x^2 - 4516108*x^3 - 4515933*x^4 - 796098*x^5 - 10159*x^6) / (1 - x)^7.
%F A160741 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 A160741 a(n) = -5 + 420*n^2 - 5040*n^4 + 14784*n^6.
%F A160741 (End)
%p A160741 A160741 := proc(n)
%p A160741         orthopoly[P](6,2*n) ;
%p A160741         numer(%) ;
%p A160741 end proc: # _R. J. Mathar_, Oct 24 2011
%t A160741 Table[Numerator[LegendreP[6,2n]],{n,0,40}]
%o A160741 (PARI) a(n)=numerator(pollegendre(6,n+n)) \\ _Charles R Greathouse IV_, Oct 24 2011
%o A160741 (PARI) Vec(-(5 - 10194*x - 795993*x^2 - 4516108*x^3 - 4515933*x^4 - 796098*x^5 - 10159*x^6) / (1 - x)^7 + O(x^30)) \\ _Colin Barker_, Jul 23 2019
%Y A160741 Cf. A160739, A144126.
%K A160741 sign,frac,easy
%O A160741 0,1
%A A160741 _N. J. A. Sloane_, Nov 17 2009