DLMF:24.6.E11 (Q7475)

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DLMF:24.6.E11
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    Statements

    Defining formula
    B n = n 2 n ⁢ ( 2 n - 1 ) ⁢ ∑ k = 1 n ∑ j = 0 k - 1 ( - 1 ) j + 1 ⁢ ( n k ) ⁢ j n - 1 , Bernoulli-number-B 𝑛 𝑛 superscript 2 𝑛 superscript 2 𝑛 1 superscript subscript 𝑘 1 𝑛 superscript subscript 𝑗 0 𝑘 1 superscript 1 𝑗 1 binomial 𝑛 𝑘 superscript 𝑗 𝑛 1 {\displaystyle{\displaystyle B_{n}=\frac{n}{2^{n}(2^{n}-1)}\sum_{k=1}^{n}\sum_% {j=0}^{k-1}(-1)^{j+1}{n\choose k}j^{n-1},}}
    0 references
    DLMF id
    DLMF:24.6.E11
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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.m1addec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1ajdec
    0 references
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1jdec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1jdec
    0 references
     
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