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 A276516 Expansion of Product_{k>=1} (1-x^(k^2)). 16
 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, 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, 0, -1, 1, -1, 2, -1, 0, 1, -2, 0, 1, 0, 1, 0, -1, 0, -2, 2, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,50 COMMENTS 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 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 Martin Klazar, What is an answer? — remarks, results and problems on PIO formulas in combinatorial enumeration, part I, arXiv:1808.08449 [math.CO], 2018. FORMULA a(n) = Sum_{k>=0} (-1)^k * A341040(n,k). - Alois P. Heinz, Feb 03 2021 MATHEMATICA nn = 15; CoefficientList[Series[Product[(1-x^(k^2)), {k, nn}], {x, 0, nn^2}], x] 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] CROSSREFS Cf. A001156, A033461, A279360, A279368, A276517, A341040. Sequence in context: A255319 A214088 A005091 * A253638 A337586 A086831 Adjacent sequences:  A276513 A276514 A276515 * A276517 A276518 A276519 KEYWORD sign,look AUTHOR Vaclav Kotesovec, Dec 12 2016 STATUS approved

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Last modified May 14 09:34 EDT 2021. Contains 343879 sequences. (Running on oeis4.)