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%I #27 Aug 28 2018 13:30:39
%S 1,-1,-2,0,0,4,1,3,0,-5,0,-7,-6,-4,7,0,6,9,11,10,-2,13,-13,-10,-17,
%T -20,-25,0,-11,-11,-2,11,41,27,41,17,58,12,27,-21,-2,-36,-67,-52,-59,
%U -95,-75,-20,-89,35,0,62,41,142,97,172,63,154,148,85,110,-36,-17,-156
%N Convolution inverse of A006171.
%H Seiichi Manyama, <a href="/A288098/b288098.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: Product_{n>=1} E(q^n) where E(q) = Product_{n>=1} (1-q^n).
%F a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A060640(k)*a(n-k) for n > 0.
%F G.f.: exp(-Sum_{k>=1} sigma(k)*x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Aug 26 2018
%t nmax = 50; CoefficientList[Series[Product[(1 - x^(i*j)), {i, 1, nmax}, {j, 1, nmax/i}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 28 2018 *)
%t nmax = 50; CoefficientList[Series[Product[(1 - x^k)^DivisorSigma[0, k], {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 28 2018 *)
%t nmax = 50; s = 1 - x; Do[s *= Sum[Binomial[DivisorSigma[0, k], j]*(-1)^j*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]];, {k, 2, nmax}]; Take[CoefficientList[s, x], nmax] (* _Vaclav Kotesovec_, Aug 28 2018 *)
%Y Cf. A006171, A060640, A107742.
%Y Product_{k>=1} (1 - x^k)^sigma_m(k): this sequence (m=0), A288385 (m=1), A288389 (m=2), A288392 (m=3).
%K sign,look
%O 0,3
%A _Seiichi Manyama_, Jun 05 2017
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