cp's OEIS Frontend

A271726 Let f(x) = 1 -x^3+ Sum_{j>=2} (x^(2^j)-x^(1+2^j)). Then a(n) is n times the coefficient of x^n in the expansion of log(f(x)).

%I A271726 #16 Apr 16 2016 11:11:27
%S A271726 0,0,-3,4,-5,-3,7,-4,-3,5,-11,1,13,-21,7,28,-51,33,19,-91,109,-33,
%T A271726 -115,209,-155,-65,321,-381,87,407,-713,476,349,-1207,1227,-35,-1739,
%U A271726 2603,-1277,-1979,4797,-4161,-903,7451,-9713,3427,9165,-18575,14021,6455,-29991,34779
%N A271726 Let f(x) = 1 -x^3+ Sum_{j>=2} (x^(2^j)-x^(1+2^j)). Then a(n) is n times the coefficient of x^n in the expansion of log(f(x)).
%C A271726 Function f(x) is connected with the density h of  exponentially (2^n)-numbers (A138302). Specifically, for h = Product_{prime p} f(1/p), this sequence allows the calculation of h with very high accuracy (cf. A271727).
%H A271726 Juan Arias-de-Reyna, <a href="/A271726/b271726.txt">Table of n, a(n) for n = 1..5000</a>
%H A271726 Vladimir Shevelev, <a href="http://arxiv.org/abs/1602.04244">A fast computation of density of exponentially S-numbers</a>, arXiv:1602.04244 [math.NT], 2016.
%t A271726 M = 6; K = 50; (* To get the first  50 terms *)
%t A271726 f = 1 - x^3 + Sum[x^(2^r) - x^(2^r + 1), {r, 2, M}];
%t A271726 S = Series[Log[f], {x, 0, K}];
%t A271726 If[2^M <= K, Print["Warning: 2^M should be greater than K and it is not. Change parameters."]];
%t A271726 L = CoefficientList[S, x];
%t A271726 A271726[n_] := n L[[n + 1]];
%t A271726 Table[A271726[n], {n, 1, K}]
%K A271726 sign
%O A271726 1,3
%A A271726 _Juan Arias-de-Reyna_, Apr 13 2016