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 A335819 #20 Aug 09 2021 06:34:47
%S A335819 1,3,12,54,270,1458,8424,51516,331452,2230740,15641424,113846472,
%T A335819 857706408,6671592216,53465326560,440602852752,3727748253456,
%U A335819 32332181692464,287111706003648,2607272929404000,24187186030419936,228997933855499808,2210786521482955392,21746223198911853504
%N A335819 E.g.f.: exp((3/2) * x * (2 + x)).
%F A335819 G.f.: 1 / (1 - 3*x - 3*x^2 / (1 - 3*x - 6*x^2 / (1 - 3*x - 9*x^2 / (1 - 3*x - 12*x^2 / (1 - ...))))), a continued fraction.
%F A335819 D-finite with recurrence a(n) = 3 * (a(n-1) + (n-1) * a(n-2)).
%F A335819 a(n) = Sum_{k=0..n} binomial(n,k) * A000085(k) * A000898(n-k).
%F A335819 a(n) = Sum_{k=0..n} binomial(n,k) * A202830(k).
%F A335819 a(n) ~ 3^(n/2) * exp(-3/4 + sqrt(3*n) - n/2) * n^(n/2) / sqrt(2). - _Vaclav Kotesovec_, Aug 09 2021
%t A335819 nmax = 23; CoefficientList[Series[Exp[(3/2) x (2 + x)], {x, 0, nmax}], x] Range[0, nmax]!
%t A335819 a[0] = 1; a[1] = 3; a[n_] := a[n] = 3 (a[n - 1] + (n - 1) a[n - 2]); Table[a[n], {n, 0, 23}]
%o A335819 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp((3*x*(2 + x)/2)))) \\ _Michel Marcus_, Nov 21 2020
%Y A335819 Cf. A000085, A000898, A202830, A294119.
%K A335819 nonn
%O A335819 0,2
%A A335819 _Ilya Gutkovskiy_, Nov 20 2020