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A099272 Unsigned member r=-14 of the family of Chebyshev sequences S_r(n) defined in A092184.

%I A099272 #16 Jul 02 2023 18:55:55
%S A099272 0,1,14,225,3584,57121,910350,14508481,231225344,3685097025,
%T A099272 58730327054,936000135841,14917271846400,237740349406561,
%U A099272 3788928318658574,60385112749130625,962372875667431424,15337580897929772161,244438921491208923150,3895685162961412998241
%N A099272 Unsigned member r=-14 of the family of Chebyshev sequences S_r(n) defined in A092184.
%C A099272 ((-1)^(n+1))*a(n) = S_{-14}(n), n>=0, defined in A092184.
%H A099272 Robert Israel, <a href="/A099272/b099272.txt">Table of n, a(n) for n = 0..831</a>
%H A099272 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A099272 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15, 15, -1).
%F A099272 a(n) = (T(n, 8)-(-1)^n)/9, with Chebyshev's polynomials of the first kind evaluated at x=8: T(n, 8)=A001081(n)=((8+3*sqrt(7))^n + (8-3*sqrt(7))^n)/2.
%F A099272 a(n) = 16*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
%F A099272 a(n) = 15*a(n-1) + 15*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=14.
%F A099272 G.f.: x*(1-x)/((1+x)*(1-16*x+x^2)) = x*(1-x)/(1-15*x-15*x^2+x^3) (from the Stephan link, see A092184).
%p A099272 f:= n -> (orthopoly[T](n,8)-(-1)^n)/9:
%p A099272 map(f, [$0..20]); # _Robert Israel_, Jun 04 2018
%t A099272 CoefficientList[Series[x (1-x)/(1-15 x-15 x^2+x^3),{x,0,33}],x] (* _Vincenzo Librandi_, Jun 05 2018 *)
%Y A099272 Cf. A001081.
%K A099272 nonn,easy
%O A099272 0,3
%A A099272 _Wolfdieter Lang_, Oct 18 2004