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%I #5 Jul 27 2020 15:46:59
%S 1,2,9,70,851,15246,384147,13065354,578905875,32440563766,
%T 2243907466283,187796863841346,18704441632101337,2186374265471576090,
%U 296396762529435076953,46126320892158605384334,8167358455139620845210003,1632571811017090501346518086
%N Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) / BesselJ(0,2*sqrt(x)).
%F a(n) = n! * Sum_{k=0..n} binomial(n,k) * A000275(k) / k!.
%t nmax = 17; CoefficientList[Series[Exp[x]/BesselJ[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2
%t A000275[0] = 1; A000275[n_] := A000275[n] = -Sum[(-1)^(n - k) Binomial[n, k]^2 A000275[k], {k, 0, n - 1}]; a[n_] := n! Sum[Binomial[n, k] A000275[k]/k!, {k, 0, n}]; Table[a[n], {n, 0, 17}]
%Y Cf. A000275, A002720, A009940, A336608.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jul 27 2020
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