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 A324591 #86 Aug 20 2021 05:47:25
%S A324591 1,2,6,24,108,552,3144,19392,129168,920736,6958944,55582848,466824384,
%T A324591 4104798336,37688879232,360236187648,3575154053376,36768528142848,
%U A324591 391060780180992,4293782854170624,48597548604926976,566152604314232832,6780179847538722816,83375209195856216064
%N A324591 E.g.f.: exp(2 * (x + x^2 / 2 + x^3 / 3)).
%F A324591 D-finite recurrence: a(n) = 2 * (a(n-1) + (n-1) * a(n-2) + (n-1) * (n-2) * a(n-3)).
%F A324591 a(n) = Sum_{k=0..n} binomial(n,k) * A057693(k) * A057693(n-k).
%t A324591 nmax = 23; CoefficientList[Series[Exp[2 (x + x^2/2 + x^3/3)], {x, 0, nmax}], x] Range[0, nmax]!
%t A324591 a[0] = 1; a[1] = 2; a[2] = 6; a[n_] := a[n] = 2 (a[n - 1] + (n - 1) a[n - 2] + (n - 1) (n - 2) a[n - 3]); Table[a[n], {n, 0, 23}]
%o A324591 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(2*(x + x^2/2 + x^3/3)))) \\ _Michel Marcus_, Nov 21 2020
%Y A324591 Cf. A000898, A057693.
%K A324591 nonn
%O A324591 0,2
%A A324591 _Ilya Gutkovskiy_, Nov 20 2020