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:
“The proof of a poet is that his country absorbs him as affectionately as he has absorbed it.”
—Walt Whitman (1819–1892)
“a meek humble Man of modest sense,
Who preaching peace does practice continence;
Whose pious life’s a proof he does believe,
Mysterious truths, which no Man can conceive.”
—John Wilmot, 2d Earl Of Rochester (1647–1680)
“Every formula which expresses a law of nature is a hymn of praise to God.”
—Maria Mitchell (1818–1889)