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G.f.: 1/(1 - x*d/dx log(eta(x))), where eta(x) is Dedekind's eta(q) function without the q^(1/24) factor.
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%I #25 Apr 07 2023 09:27:44

%S 1,-1,-2,1,2,4,-6,-5,4,1,18,-13,-26,4,22,66,-76,-78,66,37,122,-136,

%T -144,10,54,599,-368,-746,196,568,744,-938,-156,-312,-1428,2720,3340,

%U -2324,-8588,1520,8814,4846,1380,-16565,-16966,-6324,79170,47250,-160346

%N G.f.: 1/(1 - x*d/dx log(eta(x))), where eta(x) is Dedekind's eta(q) function without the q^(1/24) factor.

%H Seiichi Manyama, <a href="/A283334/b283334.txt">Table of n, a(n) for n = 0..1000</a>

%H Bernhard Heim, Markus Neuhauser, and Robert Troeger, <a href="https://arxiv.org/abs/2304.02694">Zeros Transfer For Recursively defined Polynomials</a>, arXiv:2304.02694 [math.NT], 2023. See Table 5 p. 14.

%F a(n) = -Sum_{k=0..n-1} sigma(n-k)*a(k) for n>0 with a(0) = 1.

%F G.f.: 1/(1 + Sum_{k>=1} k*x^k/(1 - x^k)). - _Ilya Gutkovskiy_, Oct 18 2018

%e G.f.: A(x) = 1 - x - 2*x^2 + x^3 + 2*x^4 + 4*x^5 - 6*x^6 - 5*x^7 + ...

%e 1/A(x) = 1 - x*d/dx log(eta(x)) = 1 + x + 3*x^2 + 4*x^3 + 7*x^4 + ... + sigma(n)*x^n + ...

%e eta(x)^3/A(x) = 1 - 2*x + 7*x^6 - 21*x^10 + 44*x^15 - 78*x^21 + ... + A184366(n)*x^n + ...

%o (PARI) lista(nn) = {va = vector(nn); va[1] = 1; for (n=1, nn-1, va[n+1] = -sum(k=0, n-1, sigma(n-k)*va[k+1]);); va;} \\ _Michel Marcus_, Mar 05 2017

%Y Cf. A180305 (1/(1 + x*d/dx log(eta(x)))), A184366.

%K sign

%O 0,3

%A _Seiichi Manyama_, Mar 05 2017