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 A335501 #7 Jul 12 2020 19:24:16
%S A335501 1,2,10,86,1098,19142,431926,12150518,414474570,16781350694,
%T A335501 792845706630,43107783435158,2666346336398454,185796230244565462,
%U A335501 14464057604306584774,1248919312238777955086,118855834572748011228490,12397162719421869533115622
%N A335501 a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} binomial(n,k)^2 * (n-k) * a(k).
%F A335501 a(n) = (n!)^2 * [x^n] exp(2 * Sum_{k>=1} x^k / (k!)^2).
%F A335501 a(n) = (n!)^2 * [x^n] exp(2 * (BesselI(0,2*sqrt(x)) - 1)).
%t A335501 a[0] = 1; a[n_] := a[n] = (2/n) Sum[Binomial[n, k]^2 (n - k) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 17}]
%t A335501 nmax = 17; CoefficientList[Series[Exp[2 Sum[x^k/(k!)^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A335501 Cf. A001861, A023998.
%K A335501 nonn
%O A335501 0,2
%A A335501 _Ilya Gutkovskiy_, Jul 12 2020