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%I #4 Dec 01 2020 17:07:24
%S 1,-1,1,-1,2,-2,1,-1,2,-3,2,-2,4,-5,4,-4,7,-8,7,-7,9,-10,8,-8,11,-14,
%T 13,-13,16,-18,17,-16,19,-22,23,-23,26,-29,29,-30,34,-38,38,-39,44,
%U -48,47,-48,56,-64,65,-66,75,-82,80,-80,90,-99,98,-100,114
%N G.f.: Product_{k>=1} (1 + (-x)^(k^2) / (1 + x^k)).
%C The difference between the number of partitions of n into an even number of parts where every part k appears at least k times and the number of partitions of n into an odd number of parts where every part k appears at least k times.
%t nmax = 60; CoefficientList[Series[Product[1 + (-x)^(k^2)/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A081362, A117144.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Dec 01 2020
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