DLMF:26.5.E1 (Q7796)

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DLMF:26.5.E1
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    Statements

    Defining formula
    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}.}}
    0 references
    DLMF id
    DLMF:26.5.E1
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1dec
    0 references
     
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