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 A336436 #6 Jul 22 2020 10:28:30
%S A336436 0,1,5,107,6020,701424,146665984,50005133576,25952660212352,
%T A336436 19469692241358336,20277424971134267904,28384315863525074792448,
%U A336436 52002222667299924427689984,121958564445078246232792363008,359324017883943122680656621023232
%N A336436 a(0) = 0; a(n) = ((n-1)!)^3 + (1/n) * Sum_{k=1..n-1} (binomial(n,k) * (n-k-1)!)^3 * k * a(k).
%F A336436 Sum_{n>=0} a(n) * x^n / (n!)^3 = -log(1 - Sum_{n>=1} x^n / n^3).
%t A336436 a[0] = 0; a[n_] := a[n] = ((n - 1)!)^3 + (1/n) Sum[(Binomial[n, k] (n - k - 1)!)^3 k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 14}]
%t A336436 nmax = 14; CoefficientList[Series[-Log[1 - Sum[x^k/k^3, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^3
%Y A336436 Cf. A003713, A074708, A193420.
%K A336436 nonn
%O A336436 0,3
%A A336436 _Ilya Gutkovskiy_, Jul 21 2020