A025171 Reciprocal Chebyshev polynomial of second kind evaluated at 4 multiplied by (-1)^n.

1, -2, -12, 56, 80, -1056, 832, 15232, -43776, -156160, 1012736, 473088, -17149952, 26730496, 220938240, -869564416, -1795883008, 17504796672, -6275465216, -267525816320, 635459076096, 3009494908928, -16186335035392, -15779248472064, 290539857510400

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..1660

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (-2,-16).

Formula

G.f.: 1/(1+2x+16x^2).

a(n) = (-2)^n*Product_{k=1..n}(1 + 4*cos(k*Pi/(n+1))). - Peter Luschny, Nov 28 2019

a(n) = -2*a(n-1)-16*a(n-2). - Christian Krause, Dec 07 2023

Maple

seq(4^n*orthopoly[U](n, -1/4), n=0..40); # Robert Israel, Nov 21 2017

Mathematica

Table[ a^n ChebyshevU[ n, -1/a ], {n, 0, 24} ]/.a->4

Prog

(PARI) a(n)=if(n<0, 0, polcoeff(1/(1+2*x+16*x^2)+x*O(x^n), n))

Crossrefs

Sequence in context: A038175 A181541 A197230 * A375885 A342319 A127214

Adjacent sequences: A025168 A025169 A025170 * A025172 A025173 A025174

Keyword

sign,easy

Author

Wouter Meeussen

Status

approved