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 A336271 #8 Feb 02 2021 23:09:45
%S A336271 1,2,10,92,1354,29252,873964,34555880,1748176714,110183215988,
%T A336271 8467704986260,779536758060920,84699429189141100,10725613123706081720,
%U A336271 1565870044943751242440,261092436660169105108592,49312362996510562406915914,10473104312824253527997052500
%N A336271 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1) * binomial(n,k)^2 * binomial(2*k,k) * a(n-k).
%F A336271 Sum_{n>=0} a(n) * x^n / (n!)^2 = 1 / BesselJ(0,2*sqrt(x))^2.
%F A336271 a(n) ~ (n!)^2 * n / (BesselJ(1, 2*sqrt(r))^2 * r^(n+1)), where r = BesselJZero(0,1)^2 / 4 = A115368^2/4 = 1.4457964907366961302939989396139517587... - _Vaclav Kotesovec_, Jul 15 2020
%t A336271 a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n, k]^2 Binomial[2 k, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]
%t A336271 nmax = 17; CoefficientList[Series[1/BesselJ[0, 2 Sqrt[x]]^2, {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A336271 Cf. A000275, A000984, A002893.
%Y A336271 Column k=2 of A340986.
%K A336271 nonn
%O A336271 0,2
%A A336271 _Ilya Gutkovskiy_, Jul 15 2020