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Expansion of x*(16*x^6+20*x^4-32*x^3+24*x^2-8*x+1) / ((-1+2*x)^2*(2*x^2-4*x+1)^2).
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%I #9 Nov 23 2017 05:38:49

%S 0,1,4,16,64,256,1024,4096,16320,64512,252416,976896,3740928,14186496,

%T 53330944,198946816,737156096,2715254784,9949593600,36292198400,

%U 131845099520,477257695232,1722054197248,6195670220800,22233100238848,79595401641984,284344067424256,1013792167690240

%N Expansion of x*(16*x^6+20*x^4-32*x^3+24*x^2-8*x+1) / ((-1+2*x)^2*(2*x^2-4*x+1)^2).

%H Colin Barker, <a href="/A294452/b294452.txt">Table of n, a(n) for n = 0..1000</a>

%H Benjamin Hackl, C. Heuberger, H. Prodinger, <a href="https://arxiv.org/abs/1612.07286">Reductions of Binary Trees and Lattice Paths induced by the Register Function</a>, arXiv preprint arXiv:1612.07286 [math.CO], 2016. (See L_2(z).)

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (12,-56,128,-148,80,-16).

%F a(n) = 12*a(n-1) - 56*a(n-2) + 128*a(n-3) - 148*a(n-4) + 80*a(n-5) - 16*a(n-6) for n>5. - _Colin Barker_, Nov 23 2017

%o (PARI) concat(0, Vec(x*(1 - 8*x + 24*x^2 - 32*x^3 + 20*x^4 + 16*x^6) / ((1 - 2*x)^2*(1 - 4*x + 2*x^2)^2) + O(x^40))) \\ _Colin Barker_, Nov 23 2017

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Nov 22 2017