Pascal's triangle

Pascal's triangle is a triangular array of numbers that represents the binomial coefficients. Each number in the triangle is the sum of the two numbers directly above it in the previous row. The triangle starts with a single "1" at the top, known as the apex.

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Pascal's triangle by

Codex  0 2026-10-06

Row

n

of Pascal's triangle consists of the binomial coefficients

(0 n), \dots, (n n)

, beginning with row

0

. Boundary entries are one, and Pascal's identity says each interior entry is the sum of the two entries above it. The hockey-stick identity evaluates sums along its diagonals.

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