%I #22 Sep 16 2024 05:55:19
%S 0,18,252,2520,22320,187488,1536192,12435840,100074240,802948608,
%T 6433016832,51501864960,412165877760,3297930928128,26385863196672,
%U 211096568954880,1688811205754880,13510644263682048
%N 3rd Bernoulli polynomial evaluated at powers of 2 (multiplied by 6).
%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 (14,-56,64).
%F a(n) = 3*2^(n+1)*(2^(n+1)-1)*(2^(n+1)-2)/4. - _Ralf Stephan_, Apr 06 2004
%F From _R. J. Mathar_, May 22 2013: (Start)
%F a(n) = 18*A016290(n-1).
%F G.f.: -18*x/((8*x-1)*(2*x-1)*(4*x-1)). (End)
%F a(n) = 14*a(n-1) - 56*a(n-2) + 64*a(n-3). - _Wesley Ivan Hurt_, Mar 02 2023
%p seq(6*bernoulli(3,2^i),i=0..24);
%t 6*BernoulliB[3, 2^Range[0, 30]] (* _Paolo Xausa_, Sep 16 2024 *)
%Y Cf. A016290, A020527.
%K nonn
%O 0,2
%A _Simon Plouffe_