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%I #20 Nov 11 2020 08:05:40
%S 1,-1,-8,-19,-9,127,500,1038,448,-4967,-21463,-50043,-59084,70418,
%T 600080,1837349,3532062,3179251,-6965009,-42260393,-119597290,
%U -224546234,-223670132,292245783,2156083245,6428174973,13030612271,16820582355,-133402359,-78307103593
%N Expansion of exp( Sum_{n>=1} -sigma_4(n)*x^n/n ) in powers of x.
%H Seiichi Manyama, <a href="/A283264/b283264.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{n>=1} (1 - x^n)^(n^3).
%F a(n) = -(1/n)*Sum_{k=1..n} sigma_4(k)*a(n-k).
%o (SageMath) # uses[EulerTransform from A166861]
%o b = EulerTransform(lambda n: -n^3)
%o print([b(n) for n in range(30)]) # _Peter Luschny_, Nov 11 2020
%Y Column k=3 of A283272.
%Y Cf. A023872 (exp( Sum_{n>=1} sigma_4(n)*x^n/n )).
%Y Cf. exp( Sum_{n>=1} -sigma_k(n)*x^n/n ): A010815 (k=1), A073592 (k=2), A283263 (k=3), this sequence (k=4), A283271 (k=5).
%K sign
%O 0,3
%A _Seiichi Manyama_, Mar 04 2017