DLMF:24.5.E6 (Q7458)

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DLMF:24.5.E6
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    Statements

    Defining formula
    ∑ k = 2 n ( n k - 2 ) ⁢ B k k = 1 ( n + 1 ) ⁢ ( n + 2 ) - B n + 1 , superscript subscript 𝑘 2 𝑛 binomial 𝑛 𝑘 2 Bernoulli-number-B 𝑘 𝑘 1 𝑛 1 𝑛 2 Bernoulli-number-B 𝑛 1 {\displaystyle{\displaystyle\sum_{k=2}^{n}{n\choose k-2}\frac{B_{k}}{k}=\frac{% 1}{(n+1)(n+2)}-B_{n+1},}}
    0 references
    DLMF id
    DLMF:24.5.E6
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    constraint
    n = 2 , 3 , … 𝑛 2 3 … {\displaystyle{\displaystyle n=2,3,\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.m1aadec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aedec
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    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1edec
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    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1edec
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