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 A336635 #5 Jul 28 2020 22:20:35
%S A336635 1,2,14,176,3470,96792,3590048,169686792,9903471502,696692504552,
%T A336635 57958925154584,5614276497440712,625153195794408608,
%U A336635 79159558899671117896,11293672011942106846808,1801015209162807119535216,318805481931592799427378062
%N A336635 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(BesselI(0,2*sqrt(x))^2 - 1).
%F A336635 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * binomial(2*k,k) * k * a(n-k).
%t A336635 nmax = 16; CoefficientList[Series[Exp[BesselI[0, 2 Sqrt[x]]^2 - 1], {x, 0, nmax}], x] Range[0, nmax]!^2
%t A336635 a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 Binomial[2 k, k] k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]
%Y A336635 Cf. A000984, A023998, A055882, A323666, A336636, A336637.
%K A336635 nonn
%O A336635 0,2
%A A336635 _Ilya Gutkovskiy_, Jul 28 2020