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%I #26 Mar 20 2017 11:26:09
%S 1,8,44,192,726,2464,7704,22527,62329,164516,416948,1019690,2416246,
%T 5565864,12498215,27421815,58903768,124088548,256749822,522450250,
%U 1046735092,2066948472,4026431543,7743987036,14715788745,27648250012,51390298666,94550761844
%N Expansion of Product_{n>=1} (1 - x^(7*n))/(1 - x^n)^8 in powers of x.
%H Seiichi Manyama, <a href="/A283077/b283077.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: exp( Sum_{n>=1} sigma(7*n)*x^n/n ).
%F a(n) = (1/n)*Sum_{k=1..n} sigma(7*k)*a(n-k). - _Seiichi Manyama_, Mar 05 2017
%F a(n) ~ 3025 * exp(sqrt(110*n/21)*Pi) / (28224*sqrt(14)*n^(5/2)). - _Vaclav Kotesovec_, Mar 20 2017
%e G.f.: A(x) = 1 + 8*x + 44*x^2 + 192*x^3 + 726*x^4 + 2464*x^5 + ...
%e log(A(x)) = 8*x + 24*x^2/2 + 32*x^3/3 + 56*x^4/4 + 48*x^5/5 + 96*x^6/6 + 57*x^7/7 + 120*x^8/8 + ... + sigma(7*n)*x^n/n + ...
%Y Cf. A282942 (Product_{n>=1} (1 - x^n)^8/(1 - x^(7*n))), A283078 (sigma(7*n)).
%Y Cf. exp( Sum_{n>=1} sigma(k*n)*x^n/n ): A182818 (k=2), A182819 (k=3), A182820 (k=4), A182821 (k=5), A283119 (k=6), this sequence (k=7), A283120 (k=8), A283121 (k=9).
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 28 2017
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