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 A330201 #7 Aug 09 2021 07:47:01
%S A330201 1,0,1,2,21,44,1045,2694,74473,421784,8776521,52518410,1843753021,
%T A330201 11476952772,387068115421,4277646186254,125796357803985,
%U A330201 1343857519264304,53205974734877713,621203524858308114,25357790175078682981,388778926109137187420
%N A330201 Expansion of e.g.f. Product_{k>=1} exp(-x^k) / (1 - x^k).
%F A330201 E.g.f.: A(x) = Product_{k>=1} B(x^k), where B(x) = e.g.f. of A000166.
%F A330201 E.g.f.: exp(Sum_{k>=1} (sigma(k) / k - 1) * x^k), where sigma = A000203.
%F A330201 E.g.f.: Product_{k>=1} 1 / (1 - x^k)^(cototient(k)/k), where cototient = A051953.
%F A330201 a(0) = 1; a(n) = (n - 1)! * Sum_{k=1..n} (sigma(k) - k) * a(n-k) / (n - k)!.
%F A330201 a(n) = Sum_{k=0..n} binomial(n,k) * A293116(k) * A053529(n-k).
%F A330201 a(n) ~ sqrt(-1/Pi + Pi/6) * n^(n - 1/2) / (2 * exp(n - 1/2 - sqrt(2*(-6 + Pi^2)*n/3))). - _Vaclav Kotesovec_, Aug 09 2021
%t A330201 nmax = 21; CoefficientList[Series[Product[Exp[-x^k]/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A330201 a[0] = 1; a[n_] := a[n] = (n - 1)! Sum[(DivisorSigma[1, k] - k) a[n - k]/(n - k)!, {k, 1, n}]; Table[a[n], {n, 0, 21}]
%Y A330201 Cf. A000166, A000203, A051953, A053529, A293116, A330200.
%K A330201 nonn
%O A330201 0,4
%A A330201 _Ilya Gutkovskiy_, Dec 05 2019