|
%I #28 Dec 07 2023 14:53:17
%S 1,-2,-12,56,80,-1056,832,15232,-43776,-156160,1012736,473088,
%T -17149952,26730496,220938240,-869564416,-1795883008,17504796672,
%U -6275465216,-267525816320,635459076096,3009494908928,-16186335035392,-15779248472064,290539857510400
%N Reciprocal Chebyshev polynomial of second kind evaluated at 4 multiplied by (-1)^n.
%H Robert Israel, <a href="/A025171/b025171.txt">Table of n, a(n) for n = 0..1660</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-16).
%F G.f.: 1/(1+2x+16x^2).
%F a(n) = (-2)^n*Product_{k=1..n}(1 + 4*cos(k*Pi/(n+1)). - _Peter Luschny_, Nov 28 2019
%F a(n) = -2*a(n-1)-16*a(n-2). - _Christian Krause_, Dec 07 2023
%p seq(4^n*orthopoly[U](n,-1/4),n=0..40); # _Robert Israel_, Nov 21 2017
%t Table[ a^n ChebyshevU[ n, -1/a ], {n, 0, 24} ]/.a->4
%o (PARI) a(n)=if(n<0,0,polcoeff(1/(1+2*x+16*x^2)+x*O(x^n),n))
%K sign,easy
%O 0,2
%A _Wouter Meeussen_
|
