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256*n^8 - 448*n^6 + 240*n^4 - 40*n^2 + 1.
2

%I #12 Sep 08 2022 08:46:08

%S 1,9,40545,1372105,15003009,93149001,409389409,1423656585,4178507265,

%T 10783446409,25154396001,54085723209,108742564225,206671502025,

%U 374437978209,651009141001,1092011153409,1775000307465,2805897612385,4326746846409,6524966384001,9644275432009

%N 256*n^8 - 448*n^6 + 240*n^4 - 40*n^2 + 1.

%C Chebyshev polynomial of the second kind U(8,n).

%H Vincenzo Librandi, <a href="/A242853/b242853.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 + 40500*x^2 + 1007440*x^3 + 4113054*x^4 + 4112928*x^5 + 1007524*x^6 + 40464*x^7 + 9*x^8)/(1 - x)^9.

%F a(n) = (2*n - 1)*(2*n + 1)*(8*n^3 - 6*n - 1) (8*n^3 - 6*n + 1).

%t Table[ChebyshevU[8, n], {n, 0, 30}] (* or *) Table[256 n^8 - 448 n^6 + 240 n^4 - 40 n^2 + 1, {n, 0, 30}]

%o (Magma) [256*n^8-448*n^6+240*n^4-40*n^2+1: n in [0..30]];

%Y Cf. A144138, A144139, A242850, A242851.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, May 30 2014