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%I #30 Aug 25 2020 01:57:26
%S 1,-1,-1,2,-2,0,4,-4,-2,6,-4,-2,10,-8,-6,14,-10,-4,20,-16,-8,24,-18,
%T -6,34,-28,-14,42,-34,-8,56,-48,-18,66,-52,-14,86,-72,-30,102,-80,-22,
%U 126,-104,-40,144,-110,-34,178,-144,-62,206,-158,-48,248,-200,-82,282,-208,-74,338,-264,-122,386,-282,-104,452,-348,-156,504
%N Expansion of x/B(x) where B(x) is the g.f. for A002487.
%C a(n) is the Euler transform of a sequence b(n) = [-1,-1,1,-1,0,1,0,-1,0,0,0,1 ...] that has (for n > 0, k > 0) b(2^k-1) = -1, b(3*2^k-1) = 1, and b(n) = 0 otherwise. - _Georg Fischer_, Aug 24 2020
%H Georg Fischer, <a href="/A073469/b073469.txt">Table of n, a(n) for n = 0..1000</a>
%H P. Dumas and P. Flajolet, <a href="https://doi.org/10.5802/jtnb.154">Asymptotique des récurrences mahlériennes: le cas cyclotomique</a>, Journal de Théorie des Nombres de Bordeaux 8 (1996), pp. 1-30.
%F This sequence grows asymptotically roughly like exp(log(n)^2), but with a complicated pattern of oscillations: see the article by Dumas-Flajolet, page 4, for a complete expansion that is related to A000123 and methods of de Bruijn. - _Philippe Flajolet_, Sep 06 2008
%F G.f. A(x) satisfies: A(x) = A(x^2) / (1 + x + x^2). - _Ilya Gutkovskiy_, Jul 09 2019
%t terms = 70; A[x_] = 1/Product[1 + x^(2^k) + x^(2^(k + 1)), {k, 0, Ceiling[ Log[2, terms]]}] + O[x]^terms; CoefficientList[A[x], x] (* _Jean-François Alcover_, Jun 30 2011, updated Jan 15 2018 *)
%K sign
%O 0,4
%A _N. J. A. Sloane_, Aug 26 2002
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