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.

A258347 Expansion of Product_{k>=1} 1/(1-x^k)^(k*(k+1)).

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%I A258347 #9 Aug 22 2018 10:34:00
%S A258347 1,2,9,28,88,250,708,1894,4988,12718,31839,77952,187771,444526,
%T A258347 1037522,2387670,5426996,12188774,27079379,59541078,129663636,
%U A258347 279801102,598620511,1270300142,2674874760,5591124784,11605082733,23926811840,49016020317,99798382290
%N A258347 Expansion of Product_{k>=1} 1/(1-x^k)^(k*(k+1)).
%H A258347 Vaclav Kotesovec, <a href="/A258347/b258347.txt">Table of n, a(n) for n = 0..1000</a>
%F A258347 a(n) ~ Pi^(1/12) / (2^(3/2) * 15^(7/48) * n^(31/48)) * exp(Zeta'(-1) - Zeta(3) / (4*Pi^2) + 75*Zeta(3)^3 / Pi^8 - 15^(5/4) * Zeta(3)^2 / (2*Pi^5) * n^(1/4) + sqrt(15) * Zeta(3) / Pi^2 * sqrt(n) + 4*Pi / (3*15^(1/4)) * n^(3/4)), where Zeta(3) = A002117, Zeta'(-1) = A084448 = 1/12 - log(A074962).
%F A258347 G.f.: exp(Sum_{k>=1} (sigma_2(k) + sigma_3(k))*x^k/k). - _Ilya Gutkovskiy_, Aug 22 2018
%t A258347 nmax=40; CoefficientList[Series[Product[1/(1-x^k)^(k*(k+1)),{k,1,nmax}],{x,0,nmax}],x]
%Y A258347 Cf. A000294, A023871, A258341, A258348, A258349, A258350, A258351, A258352.
%K A258347 nonn
%O A258347 0,2
%A A258347 _Vaclav Kotesovec_, May 27 2015