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Notation
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^  - "to the power of" (3^3 = 3 * 3 * 3 = 27)
! - factorial (for example: 4! = 1*2*3*4, and 5! = 4! * 5)
C(n, r) - n choose r, where C(n, r) = n! / [(n-r)!r!]
C(n, r1, r2, ..., rk) = n choose r1, r2, ..., rk
sqrt(x) - the square root of x
(i=p, q) - summation where i goes from p to q.