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 A346292 #5 Jul 13 2021 09:19:01
%S A346292 1,0,0,4,36,576,17600,694800,35802144,2391438336,200018045952,
%T A346292 20476348214400,2521840589347200,368057828019898368,
%U A346292 62841061478699292672,12413136137144581203456,2809529229255558769612800,722458985698006017844838400,209487621780682072569567903744
%N A346292 a(0) = 1; a(n) = (1/n) * Sum_{k=3..n} (binomial(n,k) * k!)^2 * a(n-k) / k.
%F A346292 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( polylog(2,x) - x - x^2 / 4 ).
%F A346292 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( Sum_{n>=3} x^n / n^2 ).
%t A346292 a[0] = 1; a[n_] := a[n] = (1/n) Sum[(Binomial[n, k] k!)^2 a[n - k]/k, {k, 3, n}]; Table[a[n], {n, 0, 18}]
%t A346292 nmax = 18; CoefficientList[Series[Exp[PolyLog[2, x] - x - x^2/4], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A346292 Cf. A038205, A074707, A346291.
%K A346292 nonn
%O A346292 0,4
%A A346292 _Ilya Gutkovskiy_, Jul 13 2021