%I
%S 1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,
%T 0,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,2,1,1,1,0,0,1,1,1,1,1,0,
%U 0,1,1,1,2,1,0,1,2,0,1,0,1,0,1,0,2,2,0
%N Expansion of Product_{k>=1} (1x^(k^2)).
%C The difference between the number of partitions of n into an even number of distinct squares and the number of partitions of n into an odd number of distinct squares.  _Ilya Gutkovskiy_, Jan 15 2018
%H Vaclav Kotesovec, <a href="/A276516/b276516.txt">Table of n, a(n) for n = 0..10000</a>
%H Martin Klazar, <a href="http://arxiv.org/abs/1808.08449">What is an answer? — remarks, results and problems on PIO formulas in combinatorial enumeration, part I</a>, arXiv:1808.08449 [math.CO], 2018.
%F a(n) = Sum_{k>=0} (1)^k * A341040(n,k).  _Alois P. Heinz_, Feb 03 2021
%t nn = 15; CoefficientList[Series[Product[(1x^(k^2)), {k, nn}], {x, 0, nn^2}], x]
%t nmax = 200; nn = Floor[Sqrt[nmax]]+1; poly = ConstantArray[0, nn^2 + 1]; poly[[1]] = 1; poly[[2]] = 1; poly[[3]] = 0; Do[Do[poly[[j + 1]] = poly[[j  k^2 + 1]], {j, nn^2, k^2, 1}];, {k, 2, nn}]; Take[poly, nmax+1]
%Y Cf. A001156, A033461, A279360, A279368, A276517, A341040.
%K sign,look
%O 0,50
%A _Vaclav Kotesovec_, Dec 12 2016
