login
a(n) = 512*n^9 - 1024*n^7 + 672*n^5 - 160*n^3 + 10*n.
2

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

%S 0,10,151316,7997214,118118440,922080050,4878316860,19828978246,

%T 66593931344,193501094490,501827040100,1187422368110,2605282707576,

%U 5365498355074,10470873504140,19508549760150,34910198169760,60297759323306,100934312212404,164302439443390

%N a(n) = 512*n^9 - 1024*n^7 + 672*n^5 - 160*n^3 + 10*n.

%C Chebyshev polynomial of the second kind U(9,n).

%H Vincenzo Librandi, <a href="/A242854/b242854.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F G.f.: x*(10 + 151216*x + 6484504*x^2 + 44954320*x^3 + 82614460*x^4 + 44954320*x^5 + 6484504*x^6 + 151216*x^7 + 10*x^8)/(1 - x)^10.

%F a(n) = 2*n*(4*n^2-2*n-1)*(4*n^2+2*n-1)*(16*n^4-20*n^2+5).

%p A242854:=n->512*n^9 - 1024*n^7 + 672*n^5 - 160*n^3 + 10*n: seq(A242854(n), n=0..30); # _Wesley Ivan Hurt_, Feb 04 2017

%t Table[ChebyshevU[9, n], {n, 0, 20}] (* or *) Table[512 n^9 - 1024 n^7 + 672 n^5 - 160 n^3 + 10 n, {n, 0, 20}]

%o (Magma) [512*n^9-1024*n^7+672*n^5-160*n^3+10*n: n in [0..20]];

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

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, May 30 2014