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 A337594 #5 Sep 02 2020 19:24:38
%S A337594 1,1,6,58,920,21176,654960,26114768,1298070912,78359732608,
%T A337594 5630565514496,473796572027648,46060380961356800,5114737212582603776,
%U A337594 642502387594286036992,90542358999393528670208,14209873001490130067095552,2467784343879850163370295296,471558856613839054976849608704
%N A337594 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * 4^(k-1) * a(n-k).
%F A337594 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp((BesselI(0,4*sqrt(x)) - 1) / 4).
%F A337594 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(Sum_{n>=1} 4^(n-1) * x^n / (n!)^2).
%t A337594 a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k 4^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
%t A337594 nmax = 18; CoefficientList[Series[Exp[(BesselI[0, 4 Sqrt[x]] - 1)/4], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A337594 Cf. A004213, A337592, A337593, A337595, A337597.
%K A337594 nonn
%O A337594 0,3
%A A337594 _Ilya Gutkovskiy_, Sep 02 2020