(MAGMAMagma) [64*n^6-80*n^4+24*n^2-1: n in [0..40]];

editing

approved

a(n) = (8*n^3-4*n^2-4*n+1)*(8*n^3+4*n^2-4*n-1).

Table[ChebyshevU[64 n^6, - 80 n^4 + 24 n], ^2 - 1, {n, 0, 40}] (* or *) Table[64 n^ChebyshevU[6 - 80 n^4 + 24 , n^2 - 1, ], {n, 0, 40}]

Cf. A000466, A144138, A144139, A242850.

ChebyshevU[6, n].

64*n^6 - 80*n^4 + 24*n^2 - 1.

Chebyshev polynomial of the second kind U(6,n).

a(n) = 64*n^6 - 80*n^4 + 24*n^2 - 1 = (8*n^3-4*n^2-4*n+1)*(8*n^3+4*n^2-4*n-1)

a(n) = 64*n^6 - 80*n^4 + 24*n^2 - 1. = (8*n^3-4*n^2-4*n+1)*(8*n^3+4*n^2-4*n-1)

Table[ChebyshevU[6, n], {n, 0, 40}] (* or *) CoefficientList[SeriesTable[ (- 1 + 14 x + 2841 x^2 + 20196 x64 n^3 + 20161 x6 - 80 n^4 + 2862 x^5 + 7 x24 n^6)/(2 - 1 - x)^7, , {x, n, 0, 40}], x]

(MAGMA) [(64*n^6-80*n^4+24*n^2-1): n in [0..40]];

Edited by Bruno Berselli, May 29 2014

proposed

editing

editing

proposed

G.f.: (-1 + 14*x + 2841*x^2 + 20196*x^3 + 20161*x^4 + 2862*x^5 + 7*x^6)/(1 - x)^7.

Table[ChebyshevU[6, n], {n, 0, 40}] (* or *) CoefficientList[Series[ (- 1 + 14 x + 2841 x^2 + 20196 x^3 + 20161 x^4 + 2862 x^5 + 7 x^6)/(1 - x)^7, {x, 0, 40}], x]

allocated for Vincenzo Librandi

ChebyshevU[6, n].

-1, 7, 2911, 40391, 242047, 950599, 2883167, 7338631, 16451071, 33489287, 63202399, 112211527, 189447551, 306634951, 478821727, 724955399, 1068505087, 1538129671, 2168392031, 3000519367, 4083209599, 5473483847, 7237584991, 9451922311, 12204062207, 15593764999

0,2

Vincenzo Librandi, <a href="/A242851/b242851.txt">Table of n, a(n) for n = 0..1000</a>

a(n) = 64*n^6 - 80*n^4 + 24*n^2 - 1.

Table[ChebyshevU[6, n], {n, 0, 40}]

(MAGMA) [(64*n^6-80*n^4+24*n^2-1): n in [0..40]];

Cf. A144138, A144139.

allocated

sign,easy

Vincenzo Librandi, May 29 2014

approved

editing

allocated for Vincenzo Librandi

allocated

approved