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 A346291 #6 Jul 13 2021 09:18:55
%S A346291 1,0,1,4,54,976,27050,1037016,53040344,3494603904,288738690552,
%T A346291 29267185135200,3573720291756912,517691602686711168,
%U A346291 87813773085480166608,17246816939881695262656,3883816372280829757142400,994217196872849143760818176,287129874355801742457562921344
%N A346291 a(0) = 1; a(n) = (1/n) * Sum_{k=2..n} (binomial(n,k) * k!)^2 * a(n-k) / k.
%F A346291 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( polylog(2,x) - x ).
%F A346291 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( Sum_{n>=2} x^n / n^2 ).
%t A346291 a[0] = 1; a[n_] := a[n] = (1/n) Sum[(Binomial[n, k] k!)^2 a[n - k]/k, {k, 2, n}]; Table[a[n], {n, 0, 18}]
%t A346291 nmax = 18; CoefficientList[Series[Exp[PolyLog[2, x] - x], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A346291 Cf. A000166, A074707, A346292.
%K A346291 nonn
%O A346291 0,4
%A A346291 _Ilya Gutkovskiy_, Jul 13 2021