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A283120 Expansion of exp( Sum_{n>=1} sigma(8*n)*x^n/n ) in powers of x.

%I A283120 #23 Mar 20 2017 11:28:06
%S A283120 1,15,128,815,4289,19663,81057,306799,1081986,3594142,11338690,
%T A283120 34193246,99080387,277046893,750192227,1973050940,5053026949,
%U A283120 12628736331,30859262181,73849589786,173333118663,399528823032,905418038792,2019454523623,4437187104779
%N A283120 Expansion of exp( Sum_{n>=1} sigma(8*n)*x^n/n ) in powers of x.
%H A283120 Seiichi Manyama, <a href="/A283120/b283120.txt">Table of n, a(n) for n = 0..1000</a>
%F A283120 G.f.: Product_{n>=1} (1 - x^(2*n))^7/(1 - x^n)^15.
%F A283120 a(n) = (1/n)*Sum_{k=1..n} sigma(8*k)*a(n-k). - _Seiichi Manyama_, Mar 05 2017
%F A283120 a(n) ~ 529 * 23^(1/4) * exp(sqrt(23*n/3)*Pi) / (73728 * 3^(1/4) * n^(11/4)). - _Vaclav Kotesovec_, Mar 20 2017
%e A283120 G.f.: A(x) = 1 + 15*x + 128*x^2 + 815*x^3 + 4289*x^4 + 19663*x^5 + ...
%e A283120 log(A(x)) = 15*x + 31*x^2/2 + 60*x^3/3 + 63*x^4/4 + 90*x^5/5 + 124*x^6/6 + 120*x^7/7 + 127*x^8/8 + ... + sigma(8*n)*x^n/n + ...
%Y A283120 Cf. A283122 (sigma(8*n)), A283168 (exp( Sum_{n>=1} -sigma(8*n)*x^n/n )).
%Y A283120 Cf. A182818 (k=2), A182819 (k=3), A182820 (k=4), A182821 (k=5), A283119 (k=6), A283077 (k=7), this sequence (k=8), A283121 (k=9).
%K A283120 nonn
%O A283120 0,2
%A A283120 _Seiichi Manyama_, Mar 01 2017