%I #25 Oct 18 2024 18:24:53
%S -1,119,4319,94079,1727999,29521919,487710719,7927726079,127844351999,
%T 2053539102719,32920955781119,527250311086079,8440126636031999,
%U 135075005485547519,2161463946400235519,34585534108092334079,553385433841532927999,8854302047907159736319
%N 4th Bernoulli polynomial evaluated at powers of 2 (multiplied by 30).
%H Colin Barker, <a href="/A020529/b020529.txt">Table of n, a(n) for n = 0..800</a>
%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (29,-252,736,-512).
%F a(n) = 30*16^n - 60*8^n + 30*4^n - 1.
%F From _Colin Barker_, Aug 26 2016: (Start)
%F a(n) = 29*a(n-1) - 252*a(n-2) + 736*a(n-3) - 512*a(n-4) for n > 3.
%F G.f.: -(1 - 148*x - 616*x^2 + 448*x^3)/((1-x)*(1-4*x)*(1-8*x)*(1-16*x)). (End)
%F E.g.f.: exp(x)*(30*exp(3*x)*(exp(12*x) - 2*exp(4*x) + 1) - 1). - _Elmo R. Oliveira_, Sep 16 2024
%p seq(bernoulli(4,2^i),i=0..24);
%t LinearRecurrence[{29,-252,736,-512},{-1,119,4319,94079},20] (* _Harvey P. Dale_, Feb 06 2020 *)
%o (PARI) Vec(-(1-148*x-616*x^2+448*x^3)/((1-x)*(1-4*x)*(1-8*x)*(1-16*x)) + O(x^20)) \\ _Colin Barker_, Aug 26 2016
%K sign,easy,changed
%O 0,2
%A _Simon Plouffe_