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 A336609 #4 Jul 27 2020 15:50:16
%S A336609 1,1,5,52,917,24396,909002,45062697,2862532213,226403027044,
%T A336609 21794813189810,2507115921526437,339421509956163362,
%U A336609 53393907140415300317,9653668439939308357991,1987242385193691443059527,461955240782446199029195253
%N A336609 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(1 / BesselJ(0,2*sqrt(x)) - 1).
%F A336609 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * A000275(k) * a(n-k).
%t A336609 nmax = 16; CoefficientList[Series[Exp[1/BesselJ[0, 2 Sqrt[x]] - 1], {x, 0, nmax}], x] Range[0, nmax]!^2
%t A336609 A000275[0] = 1; A000275[n_] := A000275[n] = -Sum[(-1)^(n - k) Binomial[n, k]^2 A000275[k], {k, 0, n - 1}]; a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k A000275[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]
%Y A336609 Cf. A000275, A002190, A023998.
%K A336609 nonn
%O A336609 0,3
%A A336609 _Ilya Gutkovskiy_, Jul 27 2020