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A202205
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G.f.: Sum_{n>=1} x^n * Product_{k=1..n} (1-x^k)^2.
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2
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1, 1, -1, 0, -2, 2, -1, 1, 2, -1, -1, 2, -1, -4, 3, -1, 0, -1, 0, 3, 1, -2, 0, 1, 3, -2, -3, 2, -2, 1, -1, 2, -4, -2, 5, -1, 1, 1, -4, 4, -1, 2, 1, -2, 2, -1, -1, -3, 3, 2, -1, -4, 0, 0, -1, 2, -1, 0, 2, -1, 0, -3, 5, -2, -1, 5, 3, -4, -2, 2, -4, 4, 0, 3, -2
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OFFSET
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0,5
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COMMENTS
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Compare g.f. to: (1 - eta(x))/x = Sum_{n>=0} x^n*Product_{k=1..n} (1-x^k) = 1 + x - x^4 - x^6 + x^11 + x^14 - x^21 - x^25 + x^34 + x^39 +..., where eta(q) is the Dedekind eta function without the q^(1/24) factor.
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LINKS
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EXAMPLE
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G.f.: A(x) = 1 + x - x^2 - 2*x^4 + 2*x^5 - x^6 + x^7 + 2*x^8 - x^9 - x^10 +...
where A(x) = 1 + x*(1-x)^2 + x^2*(1-x)^2*(1-x^2)^2 + x^3*(1-x)^2*(1-x^2)^2*(1-x^3)^2 +...
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PROG
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(PARI) {a(n)=polcoeff(1+sum(m=1, n, x^m*prod(k=1, m, (1-x^k +x*O(x^n))^2)), n)}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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