DLMF:24.5.E8 (Q7460)

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DLMF:24.5.E8
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    Statements

    Defining formula
    ∑ k = 0 n 2 2 ⁢ k ⁢ B 2 ⁢ k ( 2 ⁢ k ) ! ⁢ ( 2 ⁢ n + 1 - 2 ⁢ k ) ! = 1 ( 2 ⁢ n ) ! , superscript subscript 𝑘 0 𝑛 superscript 2 2 𝑘 Bernoulli-number-B 2 𝑘 2 𝑘 2 𝑛 1 2 𝑘 1 2 𝑛 {\displaystyle{\displaystyle\sum_{k=0}^{n}\frac{2^{2k}B_{2k}}{(2k)!(2n+1-2k)!}% =\frac{1}{(2n)!},}}
    0 references
    DLMF id
    DLMF:24.5.E8
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    constraint
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}
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    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1gdec
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    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1gdec
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