Integer Sequences Connected to the Laplace Continued Fraction and Ramanujan's Identity

We consider integer sequences connected to the famous Laplace continued fraction for the function R(t) = integral(infinity)(t) phi(x)dx /phi(t), where phi(l) = e(-t2)/2/root 2 pi is the standard normal density. We compute the generating functions for these sequences and study their relation to the ilermite and Bessel polynomials. Using the master equation for the generating functions, we find a new proof of the Ranianujan identity.