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%I #7 Jan 23 2018 07:57:41
%S 1,1,27,4275,2326275,3260434275,9824561849025,56272951734424425,
%T 560476093710119461875,9074718916938795106861875,
%U 226586114542199918676706160625,8362768986063791790897266120885625,440616849129306857329147873116900455625,32189976281042425371050387695609814928515625
%N G.f.: Sum_{n>=0} a(n)*x^(2*n)/((2*n)!)^2 = 1/BesselJ(0,x).
%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F a(n) = ((2*n)!)^2 * [x^(2*n)] 1/BesselJ(0,x).
%e 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 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 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 Cf. A000275, A001818, A002454.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 22 2018
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