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Formula:8489

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Digital Library of Mathematical Functions ID 26.5.E1

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}.}}


Constraint(s)

Symbols List

  • ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}} :
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
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This page was last edited on 28 January 2024, at 10:30.
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