Pascal's triangle generator
Generate Pascal's triangle — each number is the sum of the two numbers above it. Row n contains the binomial coefficients C(n,k).
Rows
Pascal's triangle
Row 0: 1. Row 1: 1 1. Row 2: 1 2 1. Row 3: 1 3 3 1. Row 4: 1 4 6 4 1...
Properties
Row n contains C(n,0), C(n,1), ..., C(n,n). Sum of row n = 2ⁿ. Diagonal patterns: natural numbers, triangular numbers, tetrahedral numbers.
Binomial theorem
(a+b)ⁿ = Σ C(n,k) × aⁿ⁻ᵏ × bᵏ. The coefficients come directly from Pascal's triangle.
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