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A322890 a(n) = value of Chebyshev T-polynomial T_n(20).

%I A322890 #26 Jan 20 2019 06:47:07
%S A322890 1,20,799,31940,1276801,51040100,2040327199,81562047860,3260441587201,
%T A322890 130336101440180,5210183616019999,208277008539359780,
%U A322890 8325870157958371201,332826529309795488260,13304735302233861159199,531856585560044650879700
%N A322890 a(n) = value of Chebyshev T-polynomial T_n(20).
%H A322890 Seiichi Manyama, <a href="/A322890/b322890.txt">Table of n, a(n) for n = 0..624</a>
%H A322890 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%H A322890 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A322890 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (40, -1).
%F A322890 a(0) = 1, a(1) = 20 and a(n) = 40*a(n-1) - a(n-2) for n > 1.
%F A322890 From _Colin Barker_, Dec 30 2018: (Start)
%F A322890 G.f.: (1 - 20*x) / (1 - 40*x + x^2).
%F A322890 a(n) = ((20+sqrt(399))^(-n) * (1+(20+sqrt(399))^(2*n))) / 2.
%F A322890 (End)
%p A322890 seq(coeff(series((1-20*x)/(1-40*x+x^2),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Dec 31 2018
%t A322890 CoefficientList[Series[(1 - 20 x)/(1 - 40 x + x^2), {x, 0, 15}], x] (* or *)
%t A322890 Array[ChebyshevT[#, 20] &, 16, 0] (* _Michael De Vlieger_, Jan 01 2019 *)
%o A322890 (PARI) {a(n) = polchebyshev(n, 1, 20)}
%o A322890 (PARI) Vec((1 - 20*x) / (1 - 40*x + x^2) + O(x^20)) \\ _Colin Barker_, Dec 30 2018
%o A322890 (GAP) a:=[1,20];; for n in [3..20] do a[n]:=40*a[n-1]-a[n-2]; od; Print(a); # _Muniru A Asiru_, Dec 31 2018
%Y A322890 Column 20 of A322836.
%Y A322890 Cf. A041758.
%K A322890 nonn,easy
%O A322890 0,2
%A A322890 _Seiichi Manyama_, Dec 29 2018