Padé approximants?

[Dirk Laurie <dirk.laurie@gmail.com>]

I can't find a built-in function that computes Padé approximants of a
power series.

e.g. pade(1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + O(x^5)) → (x^2 + 6*x
+ 12)/(x^2 - 6*x + 12)

It is of course quite easy to program for oneself in the nondegenerate
case (epsilon algorithm) but I wonder if it may be disguised as a
special case of a more general function.