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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク central binomial coefficient ： ウィキペディア英語版 central binomial coefficient In mathematics the ''n''th central binomial coefficient is defined in terms of the binomial coefficient by : $=\; \backslash frac\backslash textn\; \backslash geq\; 0.$ They are called central since they show up exactly in the middle of the even-numbered rows in Pascal's triangle. The first few central binomial coefficients starting at ''n'' = 0 are: :, , , , , , 924, 3432, 12870, 48620, … == Properties == These numbers have the generating function :$\backslash frac\; \backslash sim\; \backslash fracn\backslash rightarrow\backslash infty.$ The latter can also be easily established by means of Stirling's formula. On the other hand, it can also be used as a means to determine the constant $\backslash sqrt$ in front of the Stirling formula, by comparison. Simple bounds are given by :$\backslash frac\; \backslash leq\; \backslash leq\; 4^n\backslash textn\; \backslash geq\; 1$ Some better bounds are :$\backslash frac\; \backslash leq\; \backslash fracn\; \backslash geq\; 1$ and, if more accuracy is required, : for all $n\; \backslash geq\; 1.$ The only central binomial coefficient that is odd is 1. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「central binomial coefficient」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.