cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A301546 Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_8(k)).

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%I A301546 #11 Oct 26 2018 16:51:13
%S A301546 1,1,258,6820,105766,2182826,45173473,800612809,13879861574,
%T A301546 241973744859,4071054739686,66245877049645,1059457994097088,
%U A301546 16655445770672940,256617914952467489,3883513723831505532,57872822529451093718,849759474364551701693,12298914986733768863591
%N A301546 Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_8(k)).
%H A301546 Seiichi Manyama, <a href="/A301546/b301546.txt">Table of n, a(n) for n = 0..1169</a>
%F A301546 a(n) ~ exp(10 * 2^(7/10) * Pi * (Zeta(9)/33)^(1/10) * n^(9/10)/9 + Pi * (11/Zeta(9))^(1/10) * n^(1/10) / (480 * 2^(7/10) * 3^(9/10)) - 315*Zeta(9) / (8*Pi^8)) * (Zeta(9)/33)^(1/20) / (2^(13/20) * sqrt(5) * n^(11/20)).
%F A301546 G.f.: exp(Sum_{k>=1} sigma_9(k)*x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Oct 26 2018
%t A301546 nmax = 30; CoefficientList[Series[Product[1/(1-x^k)^DivisorSigma[8, k], {k, 1, nmax}], {x, 0, nmax}], x]
%Y A301546 Cf. A013956, A301552.
%K A301546 nonn
%O A301546 0,3
%A A301546 _Vaclav Kotesovec_, Mar 23 2018