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A283121 Expansion of exp( Sum_{n>=1} sigma(9*n)*x^n/n ) in powers of x.

%I A283121 #19 Mar 20 2017 11:29:40
%S A283121 1,13,104,633,3224,14404,58151,216294,751582,2464860,7689669,22961822,
%T A283121 65955677,182985947,492016590,1285829996,3274100475,8139933477,
%U A283121 19795490575,47165634583,110259083454,253208634687,571880965638,1271549402110,2785836824325,6019078365425
%N A283121 Expansion of exp( Sum_{n>=1} sigma(9*n)*x^n/n ) in powers of x.
%H A283121 Seiichi Manyama, <a href="/A283121/b283121.txt">Table of n, a(n) for n = 0..1000</a>
%F A283121 G.f.: Product_{n>=1} (1 - x^(3*n))^4/(1 - x^n)^13.
%F A283121 a(n) = (1/n)*Sum_{k=1..n} sigma(9*k)*a(n-k). - _Seiichi Manyama_, Mar 05 2017
%F A283121 a(n) ~ 1225 * sqrt(35) * exp(sqrt(70*n)*Pi/3) / (559872*n^3). - _Vaclav Kotesovec_, Mar 20 2017
%e A283121 G.f.: A(x) = 1 + 13*x + 104*x^2 + 633*x^3 + 3224*x^4 + 14404*x^5 + ...
%e A283121 log(A(x)) = 13*x + 39*x^2/2 + 40*x^3/3 + 91*x^4/4 + 78*x^5/5 + 120*x^6/6 + 104*x^7/7 + 195*x^8/8 + ... + sigma(9*n)*x^n/n + ...
%Y A283121 Cf. A283123 (sigma(9*n)), A283169 (exp( Sum_{n>=1} -sigma(9*n)*x^n/n )).
%Y A283121 Cf. A182818 (k=2), A182819 (k=3), A182820 (k=4), A182821 (k=5), A283119 (k=6), A283077 (k=7), A283120 (k=8), this sequence (k=9).
%K A283121 nonn
%O A283121 0,2
%A A283121 _Seiichi Manyama_, Mar 01 2017