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 A337593 #5 Sep 02 2020 19:24:32
%S A337593 1,1,5,42,573,11226,294804,9946791,417064365,21187915362,
%T A337593 1278636342660,90195692894451,7338668846348844,681052861293535251,
%U A337593 71405270562056271741,8388541745045127600597,1096298129481068449931085,158383969954582566159384786,25153555538082783169267336764
%N A337593 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * 3^(k-1) * a(n-k).
%F A337593 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp((BesselI(0,2*sqrt(3*x)) - 1) / 3).
%F A337593 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(Sum_{n>=1} 3^(n-1) * x^n / (n!)^2).
%t A337593 a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k 3^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
%t A337593 nmax = 18; CoefficientList[Series[Exp[(BesselI[0, 2 Sqrt[3 x]] - 1)/3], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A337593 Cf. A004212, A337592, A337594, A337595, A337597.
%K A337593 nonn
%O A337593 0,3
%A A337593 _Ilya Gutkovskiy_, Sep 02 2020