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 A336184 #6 Jul 11 2020 07:39:45
%S A336184 1,9,53,466,5569,82656,1474045,30664656,729036801,19499288680,
%T A336184 579487528861,18943592776032,675568129695601,26099852672860344,
%U A336184 1085904530481561645,48407032164910589056,2301727955153266523521,116286277045753464506568,6220517619913795356269725
%N A336184 a(n) = n^3 + (1/n) * Sum_{k=1..n-1} binomial(n,k) * k * a(k) * (n-k)^3.
%F A336184 E.g.f.: -log(1 - exp(x) * x * (1 + 3*x + x^2)).
%F A336184 E.g.f.: -log(1 - Sum_{k>=1} k^3 * x^k / k!).
%F A336184 a(n) ~ (n-1)! / r^n, where r = 0.336491770414014560614859141224061461582454518... is the root of the equation exp(r)*r*(1 + 3*r + r^2) = 1. - _Vaclav Kotesovec_, Jul 11 2020
%t A336184 a[n_] := a[n] = n^3 + (1/n) Sum[Binomial[n, k] k a[k] (n - k)^3, {k, 1, n - 1}]; Table[a[n], {n, 1, 19}]
%t A336184 nmax = 19; CoefficientList[Series[-Log[1 - Exp[x] x (1 + 3 x + x^2)], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%Y A336184 Cf. A000578, A279358, A300452, A305990, A308862, A336183.
%K A336184 nonn
%O A336184 1,2
%A A336184 _Ilya Gutkovskiy_, Jul 10 2020