C(n,k) = C(n, n-k)
C(n,k) = C(n-1,k-1) + C(n-1,k)
∑_k=0ⁿ C(n,k) = 2ⁿ
∑_k=0ⁿ k⋅C(n,k) = n⋅2^n-1
C(n,0)² + C(n,1)² + ... + C(n,n)² = C(2n,n)
∑_k=0ⁿ C(m,k)⋅C(r,n-k) = C(m+r,n) (Vandermonde)
P(n,k) = n!/(n-k)!
C(n+k-1,k) = multisets (n types, choose k)

∑_i=1ⁿ 1 = n
∑_i=1ⁿ i = n(n+1)/2
∑_i=1ⁿ i² = n(n+1)(2n+1)/6
∑_i=1ⁿ i³ = [n(n+1)/2]²
∑_i=1ⁿ i⁴ = n(n+1)(2n+1)(3n²+3n-1)/30
Δa_n = a_n+1 - a_n
d-th order arithmetic progression ⇔ a_n is degree-d polynomial in n