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 A298595 #9 May 04 2024 11:27:44
%S A298595 1,1,27,4275,2326275,3260434275,9824561849025,56272951734424425,
%T A298595 560476093710119461875,9074718916938795106861875,
%U A298595 226586114542199918676706160625,8362768986063791790897266120885625,440616849129306857329147873116900455625,32189976281042425371050387695609814928515625
%N A298595 G.f.: Sum_{n>=0} a(n)*x^(2*n)/((2*n)!)^2 = 1/BesselJ(0,x).
%H A298595 <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F A298595 a(n) = ((2*n)!)^2 * [x^(2*n)] 1/BesselJ(0,x).
%F A298595 a(n) ~ c * Pi * 2^(4*n+3) * n^(4*n+1) / (exp(4*n) * r^(2*n+1)), where r = BesselJZero(0, 1) = A115368 = 2.40482555769... and c = 1 / BesselJ(1, r) = 1.9262348469772531439976485375138638... - _Vaclav Kotesovec_, May 04 2024
%e A298595 1/BesselJ(0,x) = 1 + x^2/(2!)^2 + 27*x^4/(4!)^2 + 4275*x^6/(6!)^2 + 2326275*x^8/(8!)^2 + ...
%t A298595 nmax = 13; Table[(CoefficientList[Series[1/BesselJ[0, x], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!^2)[[n]], {n, 1, 2 nmax + 1, 2}]
%t A298595 nmax = 13; Table[(CoefficientList[Series[1/Hypergeometric0F1[1, -x^2/4], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!^2)[[n]], {n, 1, 2 nmax + 1, 2}]
%Y A298595 Cf. A000275, A001818, A002454.
%K A298595 nonn
%O A298595 0,3
%A A298595 _Ilya Gutkovskiy_, Jan 22 2018