\[[n]_q = \sum\limits_{i=0}^{n-1} q^i = \lim_{x \rightarrow q} \frac{1-x^n}{1-x}, [ n ] !_q = \prod_{i=1}^n [i]_q, {n \brack m}_q = \frac {[n]!_q} {[m]!_q [n - m]!_q}\\ {n \brack m}_q = {n-1 \brack m-1}_q + q^m {n-1 \brack m}_q\\ \prod_{i=0}^{n-1} (1+q^iy) = \sum\limits_{i=0}^n q^{\binom{i}{2}} {n \brack i}_q y^i\\ {n + m \brack k}_q = \sum\limits_{i=0}^k q^{(n-i)(k-i)} {n \brack i}_q {m \brack k-i}_q\\ {n + m + 1 \brack n + 1}_q = \sum\limits_{i=0}^m q^i {n + i \brack n}_q\\ \frac{1}{\prod_{i=0}^n (1-q^ix)} = \sum\limits_{i \ge 0} x^i {i+n \brack n}_q \] 标签：frac,limits,sum,brack,binomial,prod From： https://www.cnblogs.com/lprdsb/p/18004749