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Expansion of 1/(1 - Sum_{k>=2} mu(k)^2*x^k), where mu(k) is the Moebius function (A008683).
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%I #9 Dec 29 2016 14:40:17

%S 1,0,1,1,1,3,3,6,8,12,20,28,45,68,102,159,238,367,557,849,1298,1973,

%T 3015,4592,7002,10679,16276,24822,37841,57696,87971,134119,204497,

%U 311783,475370,724786,1105053,1684853,2568837,3916642,5971587,9104711,13881698,21165024,32269721,49200718,75014949,114373158,174381511

%N Expansion of 1/(1 - Sum_{k>=2} mu(k)^2*x^k), where mu(k) is the Moebius function (A008683).

%C Number of compositions (ordered partitions) into squarefree parts > 1 (A144338).

%H Robert Israel, <a href="/A280197/b280197.txt">Table of n, a(n) for n = 0..5456</a>

%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>=2} mu(k)^2*x^k).

%e a(5) = 3 because we have [5], [3, 2] and [2, 3].

%p N:= 100: # for a(0)..a(N)

%p g:= 1/(1-add(numtheory:-mobius(k)^2*x^k, k=2..N)):

%p S:= series(g,x,N+1):

%p seq(coeff(S,x,j),j=0..N); # _Robert Israel_, Dec 29 2016

%t nmax = 48; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k]^2 x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

%Y Cf. A005117, A008683, A073576, A144338, A280127, A280194.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Dec 28 2016