Generating functions
Counting and combinatorics (advanced) · Mathematics
Study notes
Q: Find the generating function for aₙ = n+1 (1, 2, 3, 4, ...). G(x) = Σ (n+1)xⁿ = 1 + 2x + 3x² + ... Known: 1/(1-x)² = Σ (n+1)xⁿ. So G(x) = 1/(1-x)². One fraction encodes the whole sequence! Coefficient of x³: 4 ✓.