DLMF:26.5.E5 (Q7800)

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DLMF:26.5.E5
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    Statements

    Defining formula
    C ⁡ ( n + 1 ) = ∑ k = 0 ⌊ n / 2 ⌋ ( n 2 ⁢ k ) ⁢ 2 n - 2 ⁢ k ⁢ C ⁡ ( k ) . Catalan-number 𝑛 1 superscript subscript 𝑘 0 𝑛 2 binomial 𝑛 2 𝑘 superscript 2 𝑛 2 𝑘 Catalan-number 𝑘 {\displaystyle{\displaystyle C\left(n+1\right)=\sum_{k=0}^{\left\lfloor n/2% \right\rfloor}\genfrac{(}{)}{0.0pt}{}{n}{2k}2^{n-2k}C\left(k\right).}}
    0 references
    DLMF id
    DLMF:26.5.E5
    0 references
    Symbols used
    Catalan number
    Defining formula
    C ⁡ ( n ) Catalan-number 𝑛 {\displaystyle{\displaystyle C\left(\NVar{n}\right)}}
    xml-id
    C26.S5.E1.m2aedec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aadec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1adec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1edec
    0 references
     
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