A243134 128*n^8 - 256*n^6 + 160*n^4 - 32*n^2 + 1.

1, 1, 18817, 665857, 7380481, 46099201, 203253121, 708158977, 2081028097, 5374978561, 12545596801, 26986755841, 54276558337, 103182433537, 186979578241, 325142092801, 545471324161, 886731088897, 1401864610177, 2161873163521, 3260441587201, 4819400974081

Offset: 0

Author

Vincenzo Librandi, May 31 2014

Keywords

• nonn
• easy

Comments

Chebyshev polynomial of the first kind T(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. A056220, A144129, A144130.

Programs

Magma

[128*n^8-256*n^6+160*n^4-32*n^2+1: n in [0..40]];

Mathematica

Table[ChebyshevT[8, n], {n, 0, 40}] (* or *) Table[128 n^8 - 256 n^6 + 160 n^4 - 32 n^2 + 1, {n, 0, 20}]
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,1,18817,665857,7380481,46099201,203253121,708158977,2081028097},30] (* Harvey P. Dale, Nov 01 2015 *)

Formula

G.f.: (1 - 8*x + 18844*x^2 + 496456*x^3 + 2065222*x^4 + 2065096*x^5 + 496540*x^6 + 18808*x^7 + x^8)/(1 - x)^9.

a(0)=1, a(1)=1, a(2)=18817, a(3)=665857, a(4)=7380481, a(5)=46099201, a(6)=203253121, a(7)=708158977, a(8)=2081028097, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)- 9*a(n-8)+ a(n-9). - Harvey P. Dale, Nov 01 2015