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Expansion of Product_{k>=1} (1-x^(k^3)).
9

%I #11 Jan 15 2018 21:05:22

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

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

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

%N Expansion of Product_{k>=1} (1-x^(k^3)).

%C The difference between the number of partitions of n into an even number of distinct cubes and the number of partitions of n into an odd number of distinct cubes. - _Ilya Gutkovskiy_, Jan 15 2018

%H Vaclav Kotesovec, <a href="/A279484/b279484.txt">Table of n, a(n) for n = 0..100000</a>

%t nn = 10; CoefficientList[Series[Product[(1-x^(k^3)), {k, nn}], {x, 0, nn^3}], x]

%t nmax = 1000; nn = Floor[nmax^(1/3)]+1; poly = ConstantArray[0, nn^3 + 1]; poly[[1]] = 1; poly[[2]] = -1; poly[[3]] = 0; Do[Do[poly[[j + 1]] -= poly[[j - k^3 + 1]], {j, nn^3, k^3, -1}];, {k, 2, nn}]; Take[poly, nmax+1]

%Y Cf. A010815, A276516.

%Y Cf. A000009, A033461, A279329.

%Y Cf. A279486.

%K sign

%O 0

%A _Vaclav Kotesovec_, Dec 13 2016