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A336606
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) / BesselJ(0,2*sqrt(x)).
1
1, 2, 9, 70, 851, 15246, 384147, 13065354, 578905875, 32440563766, 2243907466283, 187796863841346, 18704441632101337, 2186374265471576090, 296396762529435076953, 46126320892158605384334, 8167358455139620845210003, 1632571811017090501346518086
OFFSET
0,2
FORMULA
a(n) = n! * Sum_{k=0..n} binomial(n,k) * A000275(k) / k!.
MATHEMATICA
nmax = 17; CoefficientList[Series[Exp[x]/BesselJ[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 27 2020
STATUS
approved