%I #16 Jun 13 2015 00:48:54
%S 0,2,1332,166376,13651920,973242272,65499561792,4294977781376,
%T 278176525712640,17908846064302592,1149543810255025152,
%U 73678889946730981376,4718907718699422044160,302120774441963815411712,19339271338993904793894912,1237826702489967325274341376
%N a(n) = 6th Euler polynomial evaluated at 2^n.
%H Colin Barker, <a href="/A020526/b020526.txt">Table of n, a(n) for n = 0..553</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (106,-3024,22016,-32768).
%F a(n) = 106*a(n-1)-3024*a(n-2)+22016*a(n-3)-32768*a(n-4) for n>3. - _Colin Barker_, May 04 2015
%F G.f.: 2*x*(15616*x^2+560*x+1) / ((2*x-1)*(8*x-1)*(32*x-1)*(64*x-1)). - _Colin Barker_, May 04 2015
%p seq(euler(6,2**i),i=0..24);
%t Table[EulerE[6,2^n],{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%o (PARI) concat(0, Vec(2*x*(15616*x^2+560*x+1)/((2*x-1)*(8*x-1)*(32*x-1)*(64*x-1)) + O(x^100))) \\ _Colin Barker_, May 04 2015
%Y Cf. A020523 - A020525.
%K nonn,easy
%O 0,2
%A _Simon Plouffe_