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Expansion of Product_{k>=2} 1/(1 + x^k).
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%I #10 Jun 16 2018 12:16:55

%S 1,0,-1,-1,0,0,0,0,1,0,0,0,1,0,0,-1,1,0,0,-1,1,-1,0,-1,2,-1,0,-2,2,-1,

%T 1,-2,3,-2,1,-3,4,-2,2,-4,5,-3,3,-5,6,-5,4,-6,9,-6,5,-9,10,-8,8,-11,

%U 13,-11,10,-14,17,-14,13,-19,21,-18,18,-23,26,-24,23,-29,34,-30,29,-38,41,-38,39

%N Expansion of Product_{k>=2} 1/(1 + x^k).

%C The difference between the number of partitions of n into an even number of parts > 1 and the number of partitions of n into an odd number of parts > 1.

%C Convolution inverse of A025147.

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=2} 1/(1 + x^k).

%F a(n) = (-1)^n * (A000700(n) - A000700(n-1)), for n > 0. - _Vaclav Kotesovec_, Jun 06 2018

%F a(n) ~ (-1)^n * Pi * exp(Pi*sqrt(n/6)) / (2^(13/4) * 3^(3/4) * n^(5/4)). - _Vaclav Kotesovec_, Jun 06 2018

%F a(n) = A027188(n+2) - A027194(n+2). - _R. J. Mathar_, Jun 16 2018

%t nmax = 78; CoefficientList[Series[Product[1/(1 + x^k), {k, 2, nmax}], {x, 0, nmax}], x]

%Y Cf. A000700, A002865, A025147, A027349, A078616, A081362.

%K sign

%O 0,25

%A _Ilya Gutkovskiy_, Jan 22 2018