  We consider an identity relating Fibonacci numbers to Pascal's triangle
discovered by G. E. Andrews. Several authors provided proofs of this identity,
most of them rather involved or else relying on sophisticated number
theoretical arguments. We present a new proof, quite simple and based on a
Riordan array argument. The main point of the proof is the construction of a
new Riordan array from a given Riordan array, by the elimination of elements.
We extend the method and as an application we obtain other identities, some of
which are new. An important feature of our construction is that it establishes
a nice connection between the generating function of the $A-$sequence of a
certain class of Riordan arrays and hypergeometric functions.
