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A246575
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Expansion of (Product_{r>=1} (1-x^r))*x^(k^2) / Product_{i=1..k} (1-x^i)^2 with k=1.
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6
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0, 1, 1, 0, -1, -2, -2, -2, -1, 0, 1, 2, 3, 3, 3, 3, 2, 1, 0, -1, -2, -3, -4, -4, -4, -4, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -6, -6, -6, -6, -6, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 5, 4, 3
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OFFSET
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0,6
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LINKS
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FORMULA
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G.f.: x*exp( Sum_{n>=1} x^n/n * (1 - 2*x^n)/(1 - x^n) ). - Paul D. Hanna, Dec 14 2015
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MAPLE
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fGL:=proc(k) local a, i, r;
a:=x^(k^2)/mul((1-x^i)^2, i=1..k);
a:=a*mul(1-x^r, r=1..101);
series(a, x, 101);
seriestolist(%);
end; fGL(1);
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MATHEMATICA
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nmax = 100; CoefficientList[Series[x*Exp[Sum[x^k/k * (1 - 2*x^k)/(1 - x^k), {k, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 17 2015 *)
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PROG
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(PARI) {a(n) = my(A=1); A = x*exp( sum(k=1, n+1, x^k/k * (1-2*x^k)/(1 - x^k) +x*O(x^n) ) ); polcoeff(A, 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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