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 A333981 #13 Jun 10 2022 06:16:35
%S A333981 0,1,4,34,576,16296,691408,41069568,3252707328,331218217600,
%T A333981 42159307194624,6558777387076608,1224428872399488000,
%U A333981 270143735036619436032,69534931015726331203584,20651854796028308275851264,7009822878720340562163007488,2696576146784893519040303235072,1166999997199470676471689819258880
%N A333981 a(0) = 0; a(n) = 2^(n-1) + (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * 2^(k-1) * (n-k) * a(n-k).
%H A333981 G. C. Greubel, <a href="/A333981/b333981.txt">Table of n, a(n) for n = 0..245</a>
%F A333981 Sum_{n>=0} a(n) * x^n / (n!)^2 = -log((3 - BesselI(0,2*sqrt(2*x))) / 2).
%t A333981 a[0] = 0; a[n_] := a[n] = 2^(n - 1) + (1/n) Sum[Binomial[n, k]^2 2^(k - 1) (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 0, 18}]
%t A333981 nmax = 18; CoefficientList[Series[-Log[(3 - BesselI[0, 2 Sqrt[2 x]])/2], {x, 0, nmax}], x] Range[0, nmax]!^2
%o A333981 (SageMath)
%o A333981 @CachedFunction
%o A333981 def a(n): return 0 if (n==0) else 2^(n-1) + (1/n)*sum(binomial(n,k)^2 *2^(k-1)*(n-k)*a(n-k) for k in (1..n-1)) # a= A333981
%o A333981 [a(n) for n in (0..30)] # _G. C. Greubel_, Jun 09 2022
%Y A333981 Cf. A102223, A123227, A333982, A333983, A333984, A333985, A337592.
%K A333981 nonn
%O A333981 0,3
%A A333981 _Ilya Gutkovskiy_, Sep 04 2020