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A073592
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Euler transform of negative integers.
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35
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1, -1, -2, -1, 0, 4, 4, 7, 3, -2, -9, -17, -25, -24, -13, -1, 32, 61, 97, 111, 112, 74, 8, -108, -243, -392, -512, -569, -542, -358, -33, 473, 1078, 1788, 2395, 2865, 2955, 2569, 1496, -245, -2751, -5783, -9121, -12299, -14739, -15806, -14719, -10930, -3813, 6593, 20284, 36139, 53081, 68620, 80539
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: Product_{k>0} (1-x^k)^k.
a(n) = -1/n*Sum_{k=1..n} sigma[2](k)*a(n-k).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, -add(
numtheory[sigma][2](j)*a(n-j), j=1..n)/n)
end:
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MATHEMATICA
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nmax=50; CoefficientList[Series[Exp[Sum[-x^k/(k*(1-x^k)^2), {k, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 02 2015 *)
a[n_]:= a[n] = -1/n*Sum[DivisorSigma[2, k]*a[n-k], {k, 1, n}]; a[0]=1; Table[a[n], {n, 0, 100}] (* Vaclav Kotesovec, Mar 02 2015 *)
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PROG
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(SageMath) # uses[EulerTransform from A166861]
b = EulerTransform(lambda n: -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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