Proof of The Formula
There are several ways of explaining why the formula
solves the combinatorial problems listed above. The first proof below uses a generating function. The other proofs are examples of bijective proofs; they involve literally counting a collection of some kind of object to arrive at the correct formula.
Read more about this topic: Catalan Number
Famous quotes containing the words proof of, proof and/or formula:
“In the reproof of chance
Lies the true proof of men.”
—William Shakespeare (1564–1616)
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—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“So, if we must give a general formula applicable to all kinds of soul, we must describe it as the first actuality [entelechy] of a natural organized body.”
—Aristotle (384–323 B.C.)