DLMF:24.14.E2 (Q7547)

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DLMF:24.14.E2
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    Statements

    Defining formula
    ∑ k = 0 n ( n k ) ⁢ B k ⁢ B n - k = ( 1 - n ) ⁢ B n - n ⁢ B n - 1 . superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 Bernoulli-number-B 𝑘 Bernoulli-number-B 𝑛 𝑘 1 𝑛 Bernoulli-number-B 𝑛 𝑛 Bernoulli-number-B 𝑛 1 {\displaystyle{\displaystyle\sum_{k=0}^{n}{n\choose k}B_{k}B_{n-k}=(1-n)B_{n}-% nB_{n-1}.}}
    0 references
    DLMF id
    DLMF:24.14.E2
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
    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
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1adec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1adec
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