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MATHEMATICA
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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}]
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}]
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