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FORMULA
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Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int(x^n*1/8*exp(-1/(sqrt(2))*sqrt(x))*(x+sqrt(2)*sqrt(x))/x, x=0..infinity), n=0, 1...
Hypergeometric generating function: exp(4*x)*(BesselI(0, 4*x)+4*x*BesselI(0, 4*x)+4*x*BesselI(1, 4*x)), i.e. a(0)=1, and a(n)= evalf(limit(n!^2*diff(exp(4*x)*(BesselI(0, 4*x)+4*x*BesselI(0, 4*x)+4*x*BesselI(1, 4*x)), x$n), x=0)), n=1, 2...
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