According to the OEIS wiki the continued fraction $[0, 1, 2, 3, 4...]$ is equal to $\frac{I_1(2)}{I_0(2)} \approx 0.697774657964...$, where $I_n$ is the Modified Bessel Function of the First Type.
This is rather surprising to me, I can't think of a good reason why Bessel Functions ought to be involved. Why is this the case?
