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%I #14 Oct 26 2018 16:53:28
%S 1,1,33,277,1829,12763,89213,584741,3704421,22964742,139315315,
%T 826585083,4807922574,27476514016,154490531418,855490577052,
%U 4670177536402,25157218161854,133831334223869,703601883107626,3658023094714380,18817745119097343,95833879532504638
%N Expansion of Product_{k>=1} (1 + x^k)^(sigma_5(k)).
%H Seiichi Manyama, <a href="/A301549/b301549.txt">Table of n, a(n) for n = 0..2000</a>
%F a(n) ~ exp(7 * Pi^(6/7) * Zeta(7)^(1/7) * n^(6/7) / (2^(9/7) * 3^(6/7))) * (3*Zeta(7)/Pi)^(1/14) / (2^(323/504) * sqrt(7) * n^(4/7)).
%F G.f.: exp(Sum_{k>=1} sigma_6(k)*x^k/(k*(1 - x^(2*k)))). - _Ilya Gutkovskiy_, Oct 26 2018
%t nmax = 30; CoefficientList[Series[Product[(1+x^k)^DivisorSigma[5, k], {k, 1, nmax}], {x, 0, nmax}], x]
%o (PARI) x='x+O('x^99); Vec(prod(i=1, 99, (1+x^i)^sigma(i, 5))) \\ _Altug Alkan_, Mar 26 2018
%Y Cf. A001160, A107742, A301543.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 23 2018
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