負の二項定理みたいなやつ
$$ \frac 1 { (1 - x ) ^ { 1 + n } } = \sum _ { i \ge 0 } \binom { n + i } i x ^ i $$
重複組み合わせ
$$ \left \lbrace x \in \mathbb{N}^k \ \middle \vert \ x _ 1 + \dots + x _ k = n \right \rbrace = \binom { n + k - 1 } { k - 1} $$
$$ \frac 1 { (1 - x ) ^ { 1 + n } } = \sum _ { i \ge 0 } \binom { n + i } i x ^ i $$
$$ \left \lbrace x \in \mathbb{N}^k \ \middle \vert \ x _ 1 + \dots + x _ k = n \right \rbrace = \binom { n + k - 1 } { k - 1} $$
