%I #5 Sep 20 2017 20:19:27
%S 1,-1,-1,0,1,0,-1,1,2,0,-3,0,2,0,-3,0,5,0,-4,-2,4,0,-5,0,7,3,-8,-1,5,
%T 1,-10,0,13,2,-10,-3,14,-2,-17,-3,21,5,-22,0,22,4,-34,-5,33,9,-33,-10,
%U 43,6,-43,-19,52,16,-51,-13,56,24,-71,-20,64,26,-78,-24,90,24,-90,-39,112,26,-115,-37
%N Expansion of Product_{k>=1} (1 - mu(k)^2*x^k), where mu() is the Moebius function (A008683).
%C Convolution inverse of A073576.
%C The difference between the number of partitions of n into an even number of distinct squarefree parts and the number of partitions of n into an odd number of distinct squarefree parts.
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} (1 - x^A005117(k)).
%p with(numtheory):
%p b:= proc(n) option remember; `if`(n=0, 1, add(add(d*
%p abs(mobius(d)), d=divisors(j)) *b(n-j), j=1..n)/n)
%p end:
%p a:= proc(n) option remember; `if`(n=0, 1,
%p -add(b(n-i)*a(i), i=0..n-1))
%p end:
%p seq(a(n), n=0..80); # _Alois P. Heinz_, Sep 20 2017
%t nmax = 75; CoefficientList[Series[Product[1 - MoebiusMu[k]^2 x^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A005117, A008683, A046675, A073576, A087188.
%K sign
%O 0,9
%A _Ilya Gutkovskiy_, Sep 19 2017