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%I #4 Feb 05 2017 13:16:55
%S 1,3,8,19,44,99,218,473,1012,2144,4504,9395,19482,40189,82534,168829,
%T 344145,699334,1417146,2864510,5776889,11626101,23353272,46827677,
%U 93747221,187399328,374092162,745817021,1485138398,2954041789,5869650947,11651500427,23107388495,45787040997,90652188078,179340159228
%N Expansion of Sum_{i>=1} mu(i)^2*x^i / (1 - Sum_{j>=1} mu(j)^2*x^j)^2, where mu() is the Moebius function (A008683).
%C Total number of parts in all compositions (ordered partitions) of n into squarefree parts (A005117).
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: Sum_{i>=1} mu(i)^2*x^i / (1 - Sum_{j>=1} mu(j)^2*x^j)^2.
%e a(4) = 19 because we have [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2], [1, 1, 1, 1] and 2 + 2 + 3 + 2 + 3 + 3 + 4 = 19.
%t nmax = 36; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i, {i, 1, nmax}]/(1 - Sum[MoebiusMu[j]^2 x^j, {j, 1, nmax}])^2, {x, 0, nmax}], x]]
%Y Cf. A005117, A008683, A121304, A280194.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Jan 30 2017
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