%I #14 Oct 26 2018 16:50:30
%S 1,1,34,278,1896,13074,92442,607200,3866890,24062327,146637082,
%T 873517399,5101981085,29274370913,165261721720,918756928198,
%U 5035250026792,27229238821726,145412875008092,767414597651951,4004930689994100,20679955170511834,105711772783426512
%N Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_5(k)).
%H Seiichi Manyama, <a href="/A301543/b301543.txt">Table of n, a(n) for n = 0..2331</a>
%F a(n) ~ exp((7*Pi)^(6/7) * (Zeta(7)/3)^(1/7) * n^(6/7) / (3*2^(3/7)) - Zeta'(-5)/2) * (Zeta(7)/(3*Pi))^(251/3528) / (2^(251/1176) * 7^(2015/3528) * n^(2015/3528)).
%F G.f.: exp(Sum_{k>=1} sigma_6(k)*x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Oct 26 2018
%t nmax = 30; CoefficientList[Series[Product[1/(1-x^k)^DivisorSigma[5, k], {k, 1, nmax}], {x, 0, nmax}], x]
%Y Product_{k>=1} 1/(1 - x^k)^sigma_m(k): A006171 (m=0), A061256 (m=1), A275585 (m=2), A288391 (m=3), A301542 (m=4), this sequence (m=5), A301544 (m=6), A301545 (m=7), A301546 (m=8), A301547 (m=9).
%Y Cf. A001160, A301549.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 23 2018