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A279485
Expansion of Product_{k>=1} (1-x^(k^4)).
4
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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0
OFFSET
0
COMMENTS
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
LINKS
MATHEMATICA
nn = 6; CoefficientList[Series[Product[(1-x^(k^4)), {k, nn}], {x, 0, nn^4}], x]
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]
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Dec 13 2016
STATUS
approved