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 A333983 #8 Sep 04 2020 10:07:00
%S A333983 0,1,6,64,1328,46336,2423040,177379840,17314109440,2172895068160,
%T A333983 340868882825216,65356107645583360,15037174515952517120,
%U A333983 4088810357694136320000,1297103066111891262668800,474788193071044243776077824,198617395218460028950533898240,94165608216423156721014443868160
%N A333983 a(0) = 0; a(n) = 4^(n-1) + (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * 4^(k-1) * (n-k) * a(n-k).
%F A333983 Sum_{n>=0} a(n) * x^n / (n!)^2 = -log((5 - BesselI(0,4*sqrt(x))) / 4).
%t A333983 a[0] = 0; a[n_] := a[n] = 4^(n - 1) + (1/n) Sum[Binomial[n, k]^2 4^(k - 1) (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n],{n, 0, 17}]
%t A333983 nmax = 17; CoefficientList[Series[-Log[(5 - BesselI[0, 4 Sqrt[x]])/4], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A333983 Cf. A102223, A201368, A333981, A333982, A333984, A333985, A337594.
%K A333983 nonn
%O A333983 0,3
%A A333983 _Ilya Gutkovskiy_, Sep 04 2020