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%I #21 Jun 13 2015 00:48:54
%S -1,9,161,1665,14849,124929,1024001,8290305,66715649,535298049,
%T 4288675841,34334572545,274777243649,2198620602369,17590575431681,
%U 140731045904385,1125874137038849,9007096175525889,72057181721067521,576459103035981825
%N a(n) = 3rd Euler polynomial evaluated at 2^n and multiplied by 4.
%H Colin Barker, <a href="/A020523/b020523.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-44,32).
%F a(n) = 4*8^n - 6*4^n + 1.
%F a(n) = 13*a(n-1)-44*a(n-2)+32*a(n-3) for n>2. - _Colin Barker_, May 04 2015
%F G.f.: -(22*x-1) / ((x-1)*(4*x-1)*(8*x-1)). - _Colin Barker_, May 04 2015
%p seq(euler(3,2^i),i=0..24);
%t Table[EulerE[3,2^n],{n,0,40}]*4 (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%o (PARI) Vec(-(22*x-1)/((x-1)*(4*x-1)*(8*x-1)) + O(x^100)) \\ _Colin Barker_, May 04 2015
%Y Cf. A020524 - A020526.
%K sign,easy
%O 0,2
%A _Simon Plouffe_
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