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a(n) = 5th Euler polynomial evaluated at 2^n and multiplied by 2.
4

%I #18 Jun 13 2015 00:48:54

%S 1,3,847,45375,1770751,61871103,2063618047,67377381375,2177548746751,

%T 70025148104703,2246302260789247,71969633128677375,

%U 2304435634414026751,73764458297036898303,2360822953465975144447,75552099118396657893375

%N a(n) = 5th Euler polynomial evaluated at 2^n and multiplied by 2.

%H Colin Barker, <a href="/A020525/b020525.txt">Table of n, a(n) for n = 0..664</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (53,-756,2752,-2048).

%F a(n) = 53*a(n-1)-756*a(n-2)+2752*a(n-3)-2048*a(n-4) for n>3. - _Colin Barker_, May 04 2015

%F G.f.: (1444*x^2-50*x+1) / ((x-1)*(4*x-1)*(16*x-1)*(32*x-1)). - _Colin Barker_, May 04 2015

%p seq(euler(5,2**i),i=0..24);

%t Table[EulerE[5,2^n],{n,0,40}]*2 (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)

%o (PARI) Vec((1444*x^2-50*x+1)/((x-1)*(4*x-1)*(16*x-1)*(32*x-1)) + O(x^100)) \\ _Colin Barker_, May 04 2015

%Y Cf. A020523 - A020526.

%K nonn,easy

%O 0,2

%A _Simon Plouffe_