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 A305628 #23 Aug 21 2018 04:22:46
%S A305628 1,-2,0,-2,5,-2,7,-6,11,-20,13,-32,31,-50,60,-70,124,-112,192,-198,
%T A305628 295,-364,422,-616,661,-1002,1034,-1500,1737,-2208,2808,-3234,4462,
%U A305628 -4876,6735,-7464,9990,-11610,14410,-17866,20947,-27082,30493,-40056,45147,-58196,66999,-83278,99641
%N A305628 Expansion of Product_{k>=1} 1/(1 + x^k)^(k+1).
%C A305628 Convolution of A081362 and A255528.
%C A305628 Convolution inverse of A219555.
%H A305628 Vaclav Kotesovec, <a href="/A305628/b305628.txt">Table of n, a(n) for n = 0..10000</a>
%F A305628 G.f.: exp(Sum_{k>=1} (-1)^k*x^k*(2 - x^k)/(k*(1 - x^k)^2)).
%F A305628 a(n) ~ (-1)^n * exp(3 * Zeta(3)^(1/3) * n^(2/3) / 2^(5/3) + Pi^2 * n^(1/3) / (3 * 2^(7/3) * Zeta(3)^(1/3)) - 1/12 - Pi^4 / (864 * Zeta(3))) * A * Zeta(3)^(5/36) / (2^(7/9) * sqrt(3*Pi) * n^(23/36)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Aug 21 2018
%t A305628 nmax = 48; CoefficientList[Series[Product[1/(1 + x^k)^(k + 1), {k, 1, nmax}], {x, 0, nmax}], x]
%t A305628 nmax = 48; CoefficientList[Series[Exp[Sum[(-1)^k x^k (2 - x^k)/(k (1 - x^k)^2), {k, 1, nmax}]], {x,0, nmax}], x]
%t A305628 a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d) d (d + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 48}]
%Y A305628 Cf. A081362, A219555, A255528.
%K A305628 sign
%O A305628 0,2
%A A305628 _Ilya Gutkovskiy_, Aug 11 2018