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 A330200 #12 Aug 09 2021 08:36:18
%S A330200 1,2,9,52,389,3366,34477,392624,5035977,70674634,1085687921,
%T A330200 17982460332,321298513549,6121639481582,124336400707989,
%U A330200 2674237637496616,60799325536137617,1454405117742700434,36556297436871331417,961899014831786663204
%N A330200 Expansion of e.g.f. Product_{k>=1} exp(x^k) / (1 - x^k).
%F A330200 E.g.f.: A(x) = Product_{k>=1} B(x^k), where B(x) = e.g.f. of A000522.
%F A330200 E.g.f.: exp(Sum_{k>=1} (sigma(k) / k + 1) * x^k), where sigma = A000203.
%F A330200 E.g.f.: Product_{k>=1} 1 / (1 - x^k)^(phi(k)/k + 1), where phi = A000010.
%F A330200 a(0) = 1; a(n) = (n - 1)! * Sum_{k=1..n} (sigma(k) + k) * a(n-k) / (n - k)!.
%F A330200 a(n) = Sum_{k=0..n} binomial(n,k) * A000262(k) * A053529(n-k).
%F A330200 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 A330200 nmax = 19; CoefficientList[Series[Product[Exp[x^k]/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A330200 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, 19}]
%t A330200 Table[n!*Sum[LaguerreL[k, -1, -1]*PartitionsP[n-k],{k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Aug 09 2021 *)
%Y A330200 Cf. A000010, A000203, A000262, A000522, A053529, A330201, A346964.
%K A330200 nonn
%O A330200 0,2
%A A330200 _Ilya Gutkovskiy_, Dec 05 2019