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%I #9 Sep 08 2022 08:46:08
%S 1,1,18817,665857,7380481,46099201,203253121,708158977,2081028097,
%T 5374978561,12545596801,26986755841,54276558337,103182433537,
%U 186979578241,325142092801,545471324161,886731088897,1401864610177,2161873163521,3260441587201,4819400974081
%N 128*n^8 - 256*n^6 + 160*n^4 - 32*n^2 + 1.
%C Chebyshev polynomial of the first kind T(8,n).
%H Vincenzo Librandi, <a href="/A243134/b243134.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F G.f.: (1 - 8*x + 18844*x^2 + 496456*x^3 + 2065222*x^4 + 2065096*x^5 + 496540*x^6 + 18808*x^7 + x^8)/(1 - x)^9.
%F a(0)=1, a(1)=1, a(2)=18817, a(3)=665857, a(4)=7380481, a(5)=46099201, a(6)=203253121, a(7)=708158977, a(8)=2081028097, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)- 9*a(n-8)+ a(n-9). - _Harvey P. Dale_, Nov 01 2015
%t Table[ChebyshevT[8, n], {n, 0, 40}] (* or *) Table[128 n^8 - 256 n^6 + 160 n^4 - 32 n^2 + 1, {n, 0, 20}]
%t LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,1,18817,665857,7380481,46099201,203253121,708158977,2081028097},30] (* _Harvey P. Dale_, Nov 01 2015 *)
%o (Magma) [128*n^8-256*n^6+160*n^4-32*n^2+1: n in [0..40]];
%Y Cf. A056220, A144129, A144130.
%K nonn,easy
%O 0,3
%A _Vincenzo Librandi_, May 31 2014
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