Re: [理工] [離散]-排列組合
※ 引述《IDontBite (大便兔子)》之銘言：
: 從坐標原點(0,0)走到(n,n),
: 走法只能往上或往右(每步1單位),
: 自己的 y 座標必須恆小於等於 x 座標,
: (也就是必須在 x = y 這條線下方)
: 問走法有幾種?
: 答案是
: 2n
: C
: n
: _________
: (n+1)
: 想了好久都不懂為什麼, 有請高手0.0
Catalan numbers
the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects.
They are named for the Belgian mathematician Eugene Charles Catalan
The nth Catalan number is given directly in terms of binomial coefficients by
2n
: C
: n
: _________
: (n+1)
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