A243130 - OEIS

%I #14 Dec 10 2023 19:14:18

%S -1,11,564719,46611179,929944511,9127651499,58130412911,276182038859,

%T 1061324394239,3472236254411,10011386405999,26069206375211,

%U 62418042417599,139296285729899,292810020137711,584605483663499,1116034330278911,2048348816684939,3630829342034159

%N 1024*n^10 - 2304*n^8 + 1792*n^6 - 560*n^4 + 60*n^2 - 1.

%C Chebyshev polynomial of the second kind U(10,n).

%H Vincenzo Librandi, <a href="/A243130/b243130.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F G.f.: (-1 + 22*x + 564543*x^2 + 40400040*x^3 + 448278942*x^4 + 1368702180*x^5 + 1368701718*x^6 + 448279272*x^7 + 40399875*x^8 + 564598*x^9 + 11*x^10)/(1 - x)^11.

%F a(n) = (32*n^5 - 16*n^4 - 32*n^3 +12*n^2 + 6*n - 1)*(32*n^5 + 16*n^4 - 32*n^3 -12*n^2 + 6*n + 1).

%t Table[ChebyshevU[10, n], {n, 0, 20}] (* or *) Table[1024 n^10 - 2304 n^8 + 1792 n^6 - 560 n^4 + 60 n^2 - 1, {n, 0, 20}]

%t LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{-1,11,564719,46611179,929944511,9127651499,58130412911,276182038859,1061324394239,3472236254411,10011386405999},20] (* _Harvey P. Dale_, Dec 10 2023 *)

%o (Magma) [1024*n^10-2304*n^8+1792*n^6-560*n^4+60*n^2-1: n in [0..20]];

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

%K sign,easy

%O 0,2

%A _Vincenzo Librandi_, May 30 2014