Summary: We consider integer sequences connected to the famous Laplace continued fraction for the function $R(t)=\int_t^\infty\varphi(x) \mathrm{d}x/\varphi(t)$, where $\varphi(t) = e^{-t^2/2}/\sqrt{2\pi}$ is the standard normal density. We compute the generating functions for these sequences and study their relation to the Hermite and Bessel polynomials. Using the master equation for the generating functions, we find a new proof of the Ramanujan identity.

11Y05, 11Y55

continued fraction, integer sequence, Ramanujan identity