DLMF:26.5.E1 (Q7796): Difference between revisions

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Revision as of 15:25, 30 December 2019

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DLMF:26.5.E1
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    C ( n ) = 1 n + 1 ( 2 n n ) = 1 2 n + 1 ( 2 n + 1 n ) = ( 2 n n ) - ( 2 n n - 1 ) = ( 2 n - 1 n ) - ( 2 n - 1 n + 1 ) . Catalan-number 𝑛 1 𝑛 1 binomial 2 𝑛 𝑛 1 2 𝑛 1 binomial 2 𝑛 1 𝑛 binomial 2 𝑛 𝑛 binomial 2 𝑛 𝑛 1 binomial 2 𝑛 1 𝑛 binomial 2 𝑛 1 𝑛 1 {\displaystyle{\displaystyle C\left(n\right)=\frac{1}{n+1}\genfrac{(}{)}{0.0pt% }{}{2n}{n}=\frac{1}{2n+1}\genfrac{(}{)}{0.0pt}{}{2n+1}{n}=\genfrac{(}{)}{0.0pt% }{}{2n}{n}-\genfrac{(}{)}{0.0pt}{}{2n}{n-1}=\genfrac{(}{)}{0.0pt}{}{2n-1}{n}-% \genfrac{(}{)}{0.0pt}{}{2n-1}{n+1}.}}
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