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Expansion of (1+16*x)/((1+4*x)*(1-8*x)).
4

%I #21 Mar 08 2021 12:14:20

%S 1,20,112,1088,7936,66560,520192,4210688,33488896,268697600,

%T 2146435072,17184063488,137422176256,1099578736640,8795824586752,

%U 70369817919488,562945658454016,4503616807239680,36028728299487232,288230651029618688,2305841909702066176,18446748471756062720

%N Expansion of (1+16*x)/((1+4*x)*(1-8*x)).

%C Sixth moments of the Rudin-Shapiro polynomials.

%D Shalosh B. Ekhad, Explicit Generating Functions, Asymptotics, and More for the First 10 Even Moments of the Rudin-Shapiro Polynomials, Preprint, 2016.

%D Doron Zeilberger, Personal Communication to N. J. A. Sloane, Apr 15 2016.

%H Colin Barker, <a href="/A271494/b271494.txt">Table of n, a(n) for n = 0..1000</a>

%H Christophe Doche, <a href="https://doi.org/10.1090/S0025-5718-05-01736-9">Even moments of generalized Rudin-Shapiro polynomials</a>, Mathematics of computation 74.252 (2005): 1923-1935.

%H Christophe Doche and Laurent Habsieger, <a href="http://web.science.mq.edu.au/~doche/049.pdf">Moments of the Rudin-Shapiro polynomials</a>, Journal of Fourier Analysis and Applications 10.5 (2004): 497-505.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,32).

%F From _Colin Barker_, Apr 17 2016: (Start)

%F a(n) = 2^(1+3*n)-(-4)^n.

%F a(n) = 4*a(n-1) + 32*a(n-2) for n>1.

%F (End)

%F a(n) = 4^n*A014551(n+1). - _R. J. Mathar_, Mar 08 2021

%t CoefficientList[Series[(1+16x)/((1+4x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{4,32},{1,20},30] (* _Harvey P. Dale_, May 13 2017 *)

%o (PARI) Vec((1+16*x)/((1+4*x)*(1-8*x)) + O(x^50)) \\ _Colin Barker_, Apr 17 2016

%Y Cf. A246036, A271495, A271496.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Apr 15 2016