A242853 256*n^8 - 448*n^6 + 240*n^4 - 40*n^2 + 1.

1, 9, 40545, 1372105, 15003009, 93149001, 409389409, 1423656585, 4178507265, 10783446409, 25154396001, 54085723209, 108742564225, 206671502025, 374437978209, 651009141001, 1092011153409, 1775000307465, 2805897612385, 4326746846409, 6524966384001, 9644275432009

Offset: 0

Author

Vincenzo Librandi, May 30 2014

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A144138, A144139, A242850, A242851.

Programs

Magma

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

Mathematica

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}]

Formula

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.

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