coefficients is known as Pascal's rule. The pattern of numbers that forms Pascal's triangle was known well before Pascal's time. The Persian mathematician...

"Pascal's Triangle Revisited" is the twenty-fifth and final episode of the first season of Community. It originally aired in the United States on NBC...

{\displaystyle i} . A generalization of the Sierpiński triangle can also be generated using Pascal's triangle if a different modulus P {\displaystyle P} is used...

sides lie on a line (called the Pascal line). Pascal's work was so precocious that René Descartes was convinced that Pascal's father had written it. When...

In mathematics, Pascal's rule (or Pascal's formula) is a combinatorial identity about binomial coefficients. It states that for positive natural numbers...

and the trinomial distribution. Pascal's pyramid is the three-dimensional analog of the two-dimensional Pascal's triangle, which contains the binomial numbers...

left and right of Pascal's triangle, the entries (shown as blanks) are all zero. Pascal's rule also gives rise to Pascal's triangle: Row number n contains...

{n-2}{k}}+\cdots +{\binom {k+1}{k}}+{\binom {k}{k}}.} Pascal's identity Pascal's triangle Leibniz triangle Vandermonde's identity Faulhaber's formula, for sums...

{\displaystyle (1+x)^{n-1}} , via "Pascal's triangle". Blaise Pascal studied the eponymous triangle comprehensively in his Traité du triangle arithmétique. However...

entries of this triangle can be computed from Pascal's: "The terms in each row are the initial term divided by the corresponding Pascal triangle entries." In...