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A283263
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Expansion of exp( Sum_{n>=1} -sigma_3(n)*x^n/n ) in powers of x.
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11
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1, -1, -4, -5, -1, 21, 49, 81, 45, -121, -484, -997, -1344, -840, 1624, 6931, 15149, 23155, 23469, 2240, -57596, -168929, -322587, -461165, -450668, -64135, 985621, 2935044, 5718865, 8597971, 9683008, 5596899, -8414092, -37295629, -83336988, -141108721
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: Product_{n>=1} (1 - x^n)^(n^2).
a(n) = -(1/n)*Sum_{k=1..n} sigma_3(k)*a(n-k).
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MATHEMATICA
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a[n_] := If[n<1, 1, -(1/n) * Sum[DivisorSigma[3, k] a[n - k], {k, n}]]; Table[a[n], {n, 0, 35}] (* Indranil Ghosh, Mar 16 2017 *)
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PROG
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(PARI) a(n) = if(n<1, 1, -(1/n) * sum(k=1, n, sigma(k, 3) * a(n - k)));
(SageMath) # uses[EulerTransform from A166861]
b = EulerTransform(lambda n: -n^2)
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CROSSREFS
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Cf. A023871 (exp( Sum_{n>=1} sigma_3(n)*x^n/n )).
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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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