Knuth is great, but if we are going to attribute this derivation, we have to go far longer back in time. De Moivre was the first to derive a closed formula for

Knuth is great, but if we are going to attribute this derivation, we have to go far longer back in time. De Moivre was the first to derive a closed formula for the Fibonacci numbers, and he did so by "inventing" generating functions. I only have wikipedia as a source right now, as I have most of my math books, including the few on the history of mathematics I have, in boxes :) http://en.wikipedia.org/wiki/History_of_combinatorics http://en.wikipedia.org/wiki/History_of_combinatorics