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Expansion of Product_{k>=2} (1 - x^(k^2)).
1

%I #7 Jan 23 2018 08:58:44

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

%T 0,1,0,-1,0,-1,0,1,1,0,0,0,0,0,0,0,-2,-1,0,1,1,1,0,-1,0,1,0,0,0,-1,0,

%U -1,1,0,0,1,-1,-1,0,0,1,1,0,0,-2,0,0,1,0,0,-1,-1,2,1,1,0,-1,-1

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

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

%C Partial sums of A276516.

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

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

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

%t nmax = 92; CoefficientList[Series[Product[1 - x^k^2, {k, 2, Floor[Sqrt[nmax]] + 1}], {x, 0, nmax}], x]

%Y Cf. A001156, A033461, A078134, A276516, A280129, A292520, A298600.

%K sign

%O 0,50

%A _Ilya Gutkovskiy_, Jan 22 2018