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A283803 Expansion of exp( Sum_{n>=1} -A283369(n)/n*x^n ) in powers of x.

%I A283803 #12 Mar 17 2017 11:10:49
%S A283803 1,-1,-256,-531185,-4294403215,-95363000657073,-4738284730302658391,
%T A283803 -459981771468075494207385,-79227701254823507875355278590,
%U A283803 -22528320196093613328344381426130010,-9999977451048811940735941180766259658078
%N A283803 Expansion of exp( Sum_{n>=1} -A283369(n)/n*x^n ) in powers of x.
%H A283803 Seiichi Manyama, <a href="/A283803/b283803.txt">Table of n, a(n) for n = 0..120</a>
%F A283803 G.f.: Product_{k>=1} (1 - x^k)^(k^(4*k)).
%F A283803 a(n) = -(1/n)*Sum_{k=1..n} A283369(k)*a(n-k) for n > 0.
%t A283803 CoefficientList[Series[Product[(1 - x^k)^(k^(4k)), {k, 1, 10}], {x, 0, 10}], x] (* _Indranil Ghosh_, Mar 17 2017 *)
%o A283803 (PARI) A(n) = sumdiv(n, d, d^(4*d + 1));
%o A283803 a(n) = if(n<1, 1, -(1/n) * sum(k=1, n, A(k) * a(n - k)));
%o A283803 for(n=0, 10, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 17 2017
%Y A283803 Cf. Product_{k>=1} (1 - x^k)^(k^(m*k)): A010815 (m=0), A283499 (m=1), A283534 (m=2), A283536 (m=3), this sequence (m=4).
%Y A283803 Cf. A283510 (Product_{k>=1} 1/(1 - x^k)^(k^(4*k))).
%K A283803 sign
%O A283803 0,3
%A A283803 _Seiichi Manyama_, Mar 17 2017