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 A337590 #4 Sep 02 2020 19:24:15
%S A337590 0,1,0,-3,28,-215,-174,90223,-3840472,103719537,429704110,
%T A337590 -357346077869,35100093531900,-2005608652057595,-24108041118593418,
%U A337590 27881407632242902515,-4876442148527153942384,474102062424164433715937,12637408141631813073125094,-18867461801192524662360616421
%N A337590 a(0) = 0; a(n) = n - (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * (n-k) * k * a(k).
%F A337590 Sum_{n>=0} a(n) * x^n / (n!)^2 = log(1 + sqrt(x) * BesselI(1,2*sqrt(x))).
%F A337590 Sum_{n>=0} a(n) * x^n / (n!)^2 = log(1 + Sum_{n>=1} n * x^n / (n!)^2).
%t A337590 a[0] = 0; a[n_] := a[n] = n - (1/n) Sum[Binomial[n, k]^2 (n - k) k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 19}]
%t A337590 nmax = 19; CoefficientList[Series[Log[1 + Sqrt[x] BesselI[1, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A337590 Cf. A002190, A009306, A336227.
%K A337590 sign
%O A337590 0,4
%A A337590 _Ilya Gutkovskiy_, Sep 02 2020