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%I #10 Sep 08 2024 12:10:26
%S 0,1,18,361,7200,143641,2865618,57168721,1140508800,22753007281,
%T 453919636818,9055639729081,180658874944800,3604121859166921,
%U 71901778308393618,1434431444308705441,28616727107865715200
%N Unsigned member r=-18 of the family of Chebyshev sequences S_r(n) defined in A092184.
%C ((-1)^(n+1))*a(n) = S_{-18}(n), n>=0, defined in A092184.
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,19,-1)>
%F a(n)= 20*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
%F a(n)= 19*a(n-1) + 19*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=18.
%F G.f.: x*(1-x)/((1+x)*(1-20*x+x^2)) = x*(1-x)/(1-19*x-19*x^2+x^3) (from the Stephan link, see A092184).
%F a(n)= (T(n, 10)-(-1)^n)/11, with Chebyshev's polynomials of the first kind evaluated at x=10: T(n, 10)=A001085(n)=((10+3*sqrt(11))^n + (10-3*sqrt(11))^n)/2.
%t LinearRecurrence[{19,19,-1},{0,1,18},30] (* _Harvey P. Dale_, Sep 08 2024 *)
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Oct 18 2004