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%I #26 Dec 04 2017 09:32:57
%S 6,780,30744,1032240,33423456,1072693440,34351350144,1099444519680,
%T 35183835219456,1125895611878400,36028762659231744,
%U 1152921229728952320,36893485948395872256,1180591603125225308160,37778931722219673452544,1208925818488729268060160
%N a(n) = 5th Chebyshev polynomial (second kind) evaluated at 2^n.
%H Colin Barker, <a href="/A020542/b020542.txt">Table of n, a(n) for n = 0..663</a>
%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 (42,-336,512).
%F From _Colin Barker_, May 03 2015: (Start)
%F a(n) = 2^(1+n)*(3-4^(2+n)+16^(1+n))
%F a(n) = 42*a(n-1)-336*a(n-2)+512*a(n-3) for n>2.
%F G.f.: -6*(88*x+1) / ((2*x-1)*(8*x-1)*(32*x-1)).
%F (End)
%p with(orthopoly):seq(U(5,2^i),i=0..24);
%t Table[ChebyshevU[5,2^n],{n,1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%t LinearRecurrence[{42, -336, 512}, {6, 780, 30744}, 16] (* _Jean-François Alcover_, Dec 04 2017 *)
%o (PARI) Vec(-6*(88*x+1)/((2*x-1)*(8*x-1)*(32*x-1)) + O(x^100)) \\ _Colin Barker_, May 03 2015
%o (PARI) a(n) = polchebyshev(5, 2, 2^n) \\ _Michel Marcus_, May 03 2015
%K nonn,easy
%O 0,1
%A _Simon Plouffe_
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