  The exponential generating function of ordinary generating functions of
diagonal sequences of general Sheffer triangles is computed by an application
of Lagrange's theorem. For the special Jabotinsky type this is already known.
An analogous computation for general Riordan number triangles leads to a
formula for the logarithmic generating function of the ordinary generating
functions of the product of the entries of the diagonal sequence of Pascal's
triangle and those of the {Riordan triangle. For some examples these ordinary
generating functions yield in both cases coefficient triangles of certain
numerator polynomials.
