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%I #4 Dec 29 2016 05:21:56
%S 1,1,1,2,3,5,8,13,21,33,53,86,138,222,357,574,923,1484,2387,3839,6173,
%T 9927,15964,25672,41284,66389,106762,171686,276091,443989,713988,
%U 1148179,1846411,2969252,4774918,7678647,12348195,19857396,31933099,51352294,82580715,132799801,213558181,343427445,552272966,888121883,1428207656
%N Expansion of 1/(1 - Sum_{k>=1} mu(2*k-1)^2*x^(2*k-1)), where mu() is the Moebius function (A008683).
%C Number of compositions (ordered partitions) into odd squarefree parts (A056911).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: 1/(1 - Sum_{k>=1} mu(2*k-1)^2*x^(2*k-1)).
%e a(4) = 3 because we have [3, 1], [1, 3] and [1, 1, 1, 1].
%t nmax = 46; CoefficientList[Series[1/(1 - Sum[MoebiusMu[2 k - 1]^2 x^(2 k - 1), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A005117, A008683, A056911, A134345, A280194.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Dec 28 2016
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