%I #31 Sep 16 2024 05:55:58

%S 1,13,73,337,1441,5953,24193,97537,391681,1569793,6285313,25153537,

%T 100638721,402604033,1610514433,6442254337,25769410561,103078428673,

%U 412315287553,1649264295937,6597063475201,26388266483713,105553091100673,422212414734337,1688849759600641,6755399239729153

%N 2nd Bernoulli polynomial evaluated at powers of 2 (multiplied by 6).

%H Vincenzo Librandi, <a href="/A020527/b020527.txt">Table of n, a(n) for n = 0..170</a>

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).

%F a(n) = 6*(4^n - 2^n) + 1. - _Ralf Stephan_, Apr 06 2004

%F G.f.: (-1 - 6*x + 4*x^2)/((x-1)*(2*x-1)*(4*x-1)). - _R. J. Mathar_, Jun 11 2013

%F From _Elmo R. Oliveira_, Sep 12 2024: (Start)

%F E.g.f.: exp(x)*(6*exp(x)*(exp(2*x) - 1) + 1).

%F a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n > 2. (End)

%p seq(6*bernoulli(2,2^i),i=0..24);

%t 6*BernoulliB[2, 2^Range[0, 30]] (* _Paolo Xausa_, Sep 16 2024 *)

%o (Magma) [6 * (4^n - 2^n) + 1: n in [0..40]]; // _Vincenzo Librandi_, Apr 25 2011

%Y Cf. A020528.

%K nonn,easy

%O 0,2

%A _Simon Plouffe_