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 A337154 #12 Jan 28 2021 11:12:27
%S A337154 1,3,49,1763,112833,11283299,1624795057,318459831171,81525716779777,
%T A337154 26414332236647747,10565732894659098801,5113814721015003819683,
%U A337154 2945557279304642200137409,1991196720809938127292888483,1561098229114991491797624570673,1404988406203492342617862113605699
%N A337154 a(n) = 4^n * (n!)^2 * Sum_{k=0..n} 1 / ((-4)^k * (k!)^2).
%F A337154 Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselJ(0,2*sqrt(x)) / (1 - 4*x).
%F A337154 a(0) = 1; a(n) = 4 * n^2 * a(n-1) + (-1)^n.
%t A337154 Table[4^n n!^2 Sum[1/((-4)^k k!^2), {k, 0, n}], {n, 0, 15}]
%t A337154 nmax = 15; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - 4 x), {x, 0, nmax}], x] Range[0, nmax]!^2
%o A337154 (PARI) a(n) = 4^n * (n!)^2 * sum(k=0, n, 1 / ((-4)^k * (k!)^2)); \\ _Michel Marcus_, Jan 28 2021
%Y A337154 Cf. A001907, A073701, A336807, A337152, A337153, A337155.
%K A337154 nonn
%O A337154 0,2
%A A337154 _Ilya Gutkovskiy_, Jan 27 2021