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%I #7 Jan 28 2018 11:01:53
%S 1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0
%N Expansion of Product_{k>=1} (1-x^(k^4)).
%C The difference between the number of partitions of n into an even number of distinct fourth powers and the number of partitions of n into an odd number of distinct fourth powers. - _Ilya Gutkovskiy_, Jan 27 2018
%H Vaclav Kotesovec, <a href="/A279485/b279485.txt">Table of n, a(n) for n = 0..100000</a>
%t nn = 6; CoefficientList[Series[Product[(1-x^(k^4)), {k, nn}], {x, 0, nn^4}], x]
%t nmax = 1000; nn = Floor[nmax^(1/4)]+1; poly = ConstantArray[0, nn^4 + 1]; poly[[1]] = 1; poly[[2]] = -1; poly[[3]] = 0; Do[Do[poly[[j + 1]] -= poly[[j - k^4 + 1]], {j, nn^4, k^4, -1}];, {k, 2, nn}]; Take[poly, nmax+1]
%Y Cf. A010815, A276516, A279484.
%Y Cf. A000009, A033461, A279329.
%K sign
%O 0
%A _Vaclav Kotesovec_, Dec 13 2016