A167440 - OEIS

%I #7 Jul 03 2023 11:20:16

%S 2,724,30248,1028176,33390752,1072431424,34349253248,1099427742976,

%T 35183701002752,1125894538138624,36028754069301248,

%U 1152921161009483776,36893485398640074752,1180591598727178829824,37778931687035301429248

%N 5th GegenbauerC polynomial evaluated at powers of 2 (multiplied by 5).

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Gegenbauer_polynomials">Gegenbauer Polynomials</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (42, -336, 512).

%F Conjectures from _Colin Barker_, Oct 27 2014: (Start)

%F a(n) = 2^n*(5-5*4^n+16^n).

%F a(n) = 42*a(n-1)-336*a(n-2)+512*a(n-3).

%F G.f.: -2*x*(256*x^2+320*x+1) / ((2*x-1)*(8*x-1)*(32*x-1)).

%F (End)

%t Table[GegenbauerC[5,2^n],{n,0,30}]*5

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009