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...

{\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...

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

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...

"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...

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...

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

{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...

In mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem. Let m...