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.
%I A275585 #45 Oct 28 2018 03:47:23
%S A275585 1,1,6,16,52,128,373,913,2399,5796,14298,33655,79756,183078,419846,
%T A275585 942807,2106176,4633208,10127557,21870997,46912648,99639685,210206722,
%U A275585 439777198,914157490,1886428608,3869204040,7884691072,15976273573,32182538964,64484592372,128518359868,254868985099,502950483815,987904826874,1931596634076
%N A275585 Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_2(k)).
%C A275585 Euler transform of the sum of squares of divisors (A001157).
%H A275585 Seiichi Manyama, <a href="/A275585/b275585.txt">Table of n, a(n) for n = 0..10000</a>
%H A275585 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A275585 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H A275585 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A275585 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F A275585 G.f.: Product_{k>=1} 1/(1 - x^k)^(sigma_2(k)).
%F A275585 a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A027847(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Jun 08 2017
%F A275585 a(n) ~ exp(4*Pi * Zeta(3)^(1/4) * n^(3/4) / (3^(5/4) * 5^(1/4)) - Pi * 5^(1/4) * n^(1/4) / (8 * 3^(7/4) * Zeta(3)^(1/4)) + Zeta(3) / (8*Pi^2)) * Zeta(3)^(1/8) / (2^(3/2) * 15^(1/8) * n^(5/8)). - _Vaclav Kotesovec_, Mar 23 2018
%F A275585 G.f.: exp(Sum_{k>=1} sigma_3(k)*x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Oct 26 2018
%p A275585 with(numtheory):
%p A275585 a:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A275585 d*sigma[2](d), d=divisors(j))*a(n-j), j=1..n)/n)
%p A275585 end:
%p A275585 seq(a(n), n=0..40); # _Alois P. Heinz_, Jun 08 2017
%t A275585 nmax = 35; CoefficientList[Series[Product[1/(1 - x^k)^(DivisorSigma[2, k]), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A275585 Cf. A001157, A027847, A288414.
%Y A275585 Product_{k>=1} 1/(1 - x^k)^sigma_m(k): A006171 (m=0), A061256 (m=1), this sequence (m=2), A288391 (m=3), A301542 (m=4), A301543 (m=5), A301544 (m=6), A301545 (m=7), A301546 (m=8), A301547 (m=9).
%K A275585 nonn
%O A275585 0,3
%A A275585 _Ilya Gutkovskiy_, Dec 25 2016