A242850 - OEIS

%I #9 Sep 08 2022 08:46:08

%S 0,6,780,6930,30744,96030,241956,526890,1032240,1866294,3168060,

%T 5111106,7907400,11811150,17122644,24192090,33423456,45278310,

%U 60279660,79015794,102144120,130395006,164575620,205573770,254361744,312000150,379641756,458535330,550029480,655576494

%N 32*n^5 - 32*n^3 + 6*n.

%C Chebyshev polynomial of the second kind U(5,n).

%H Vincenzo Librandi, <a href="/A242850/b242850.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: x*(6 + 744*x + 2340*x^2 + 744*x^3 + 6*x^4)/(1 - x)^6.

%F a(n) = 2*n*(2*n-1)*(2*n+1)*(4*n^2-3).

%t Table[32 n^5 - 32 n^3 + 6 n, {n, 0, 40}] (* or *) Table[ChebyshevU[5, n], {n, 0, 40}]

%o (Magma) [32*n^5-32*n^3+6*n: n in [0..40]];

%Y Cf. A000466, A144138, A144139, A242851.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, May 29 2014

%E Edited by _Bruno Berselli_, May 29 2014