A242854 a(n) = 512*n^9 - 1024*n^7 + 672*n^5 - 160*n^3 + 10*n.

0, 10, 151316, 7997214, 118118440, 922080050, 4878316860, 19828978246, 66593931344, 193501094490, 501827040100, 1187422368110, 2605282707576, 5365498355074, 10470873504140, 19508549760150, 34910198169760, 60297759323306, 100934312212404, 164302439443390

Offset: 0

Author

Vincenzo Librandi, May 30 2014

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A144138, A144139, A242850, A242851.

Programs

Magma

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

Maple

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

Mathematica

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}]

Formula

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.

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