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 A346220 #5 Jul 12 2021 18:01:25
%S A346220 1,1,2,7,40,321,3356,45123,752256,15018433,355378732,9823042923,
%T A346220 311510611072,11242338245009,458052976883672,20851748359005567,
%U A346220 1054108827258438656,58860837547461314049,3606677286494115444812,241397002229305033296603,17579096976247770110062080
%N A346220 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( (BesselI(0,2*sqrt(x)) - BesselJ(0,2*sqrt(x))) / 2 ).
%F A346220 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( Sum_{n>=0} x^(2*n+1) / ((2*n + 1)!)^2 ).
%F A346220 a(0) = 1; a(n) = (1/n) * Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1)^2 * (2*k+1) * a(n-2*k-1).
%t A346220 nmax = 20; CoefficientList[Series[Exp[(BesselI[0, 2 Sqrt[x]] - BesselJ[0, 2 Sqrt[x]])/2], {x, 0, nmax}], x] Range[0, nmax]!^2
%t A346220 a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, 2 k + 1]^2 (2 k + 1) a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 20}]
%Y A346220 Cf. A003724, A023998.
%K A346220 nonn
%O A346220 0,3
%A A346220 _Ilya Gutkovskiy_, Jul 11 2021